Compute the final expected value of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, using the tetraparametric function approach.

Description

Compute the final expected value of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, using the tetraparametric function approach.

Usage

FV_post_artan(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Source

Cruz Rambaud, S.; Maturo, F. and Sánchez Pérez A. M. (2017): Expected present and final value of an annuity when some non-central moments of the capitalization factor are unknown: Theory and an application using R. In Š. Hošková-Mayerová, et al. (Eds.), Mathematical-Statistical Models and Qualitative Theories for Economic and Social Sciences (pp. 233-248). Springer, Cham. doi:10.1007/978-3-319-54819-7_16.

Examples

#example 1
data=c(0.298,0.255,0.212,0.180,0.165,0.163,0.167,0.161,0.154,
0.128,0.079,0.059,0.042,-0.008,-0.012,-0.002)
FV_post_artan(data,6)

# example 2
data<-rnorm(n=30,m=0.03,sd=0.01)
FV_post_artan(data,10)

Compute the final expected value of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, using the estimated moments of the beta distribution.

Description

Compute the final expected value of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, using the estimated moments of the beta distribution.

Usage

FV_post_beta_kmom(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Source

Cruz Rambaud, S.; Maturo, F. and Sánchez Pérez A. M. (2015): “Approach of the value of an annuity when non-central moments of the capitalization factor are known: an R application with interest rates following normal and beta distributions”. Ratio Mathematica, 28(1), pp. 15-30. doi: 10.23755/rm.v28i1.25.

Examples

# example 1
data=c(0.00,-0.05,-0.05,-0.06,-0.06,0.02,-0.06,-0.05,-0.04,-0.05,
-0.03,-0.06,0.04,-0.05,-0.08,-0.05,-0.12,-0.03,-0.05,-0.04,-0.06)
FV_post_beta_kmom(data,8)

# example 2
data<-rnorm(n=200,m=0.075,sd=0.2)
FV_post_beta_kmom(data,8)

Compute the final expected value of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, using the method of Mood et al.

Description

Compute the final expected value of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, using the method of Mood et al.

Usage

FV_post_mood(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Source

Cruz Rambaud, S.; Maturo, F. and Sánchez Pérez A. M. (2017): “Expected present and final value of an annuity when some non-central moments of the capitalization factor are unknown: Theory and an application using R”. In Š. Hošková-Mayerová, et al. (Eds.), Mathematical-Statistical Models and Qualitative Theories for Economic and Social Sciences (pp. 233-248). Springer, Cham. doi:10.1007/978-3-319-54819-7_16.

Examples

#example 1
data=c(0.298,0.255,0.212,0.180,0.165,0.163,0.167,0.161,0.154,
0.128,0.079,0.059,0.042,-0.008,-0.012,-0.002)
FV_post_mood(data,6)

# example 2
data<-rnorm(n=30,m=0.03,sd=0.01)
FV_post_mood(data,10)

Compute the final expected value of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, using the estimated moments of the normal distribution.

Description

Compute the final expected value of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, using the estimated moments of the normal distribution.

Usage

FV_post_norm_kmom(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Source

Cruz Rambaud, S.; Maturo, F. and Sánchez Pérez A. M. (2015): “Approach of the value of an annuity when non-central moments of the capitalization factor are known: an R application with interest rates following normal and beta distributions”. Ratio Mathematica, 28(1), pp. 15-30. doi: 10.23755/rm.v28i1.25.

Examples

# example 1
data = c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
data=data/100
FV_post_norm_kmom(data,8)


# example 1
data<-rnorm(n=200,m=0.075,sd=0.2)
norm_test_jb(data) #test data
FV_post_norm_kmom(data,8)

Compute the final expected value of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, using the quadratic discount method.

Description

Compute the final expected value of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, using the quadratic discount method.

Usage

FV_post_quad(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Source

Cruz Rambaud, S.; Maturo, F. and Sánchez Pérez A. M. (2017): “Expected present and final value of an annuity when some non-central moments of the capitalization factor are unknown: Theory and an application using R”. In Š. Hošková-Mayerová, et al. (Eds.), Mathematical-Statistical Models and Qualitative Theories for Economic and Social Sciences (pp. 233-248). Springer, Cham. doi:10.1007/978-3-319-54819-7_16.

Examples

#example 1
data=c(0.298,0.255,0.212,0.180,0.165,0.163,0.167,0.161,0.154,
0.128,0.079,0.059,0.042,-0.008,-0.012,-0.002)
FV_post_quad(data,8)

# example 2
data<-rnorm(n=30,m=0.03,sd=0.01)
FV_post_quad(data,10)

Compute the final expected value of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, using the tetraparametric function approach.

Description

Compute the final expected value of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, using the tetraparametric function approach.

Usage

FV_pre_artan(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Source

Cruz Rambaud, S.; Maturo, F. and Sánchez Pérez A. M. (2017): “Expected present and final value of an annuity when some non-central moments of the capitalization factor are unknown: Theory and an application using R”. In Š. Hošková-Mayerová, et al. (Eds.), Mathematical-Statistical Models and Qualitative Theories for Economic and Social Sciences (pp. 233-248). Springer, Cham. doi:10.1007/978-3-319-54819-7_16.

Examples

#example 1
data=c(0.298,0.255,0.212,0.180,0.165,0.163,0.167,0.161,0.154,
0.128,0.079,0.059,0.042,-0.008,-0.012,-0.002)
FV_pre_artan(data,6)

# example 2
data<-rnorm(n=30,m=0.03,sd=0.01)
FV_pre_artan(data,10)

Compute the final expected value of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, using the estimated moments of the beta distribution.

Description

Compute the final expected value of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, using the estimated moments of the beta distribution.

Usage

FV_pre_beta_kmom(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Source

Cruz Rambaud, S.; Maturo, F. and Sánchez Pérez A. M. (2015): “Approach of the value of an annuity when non-central moments of the capitalization factor are known: an R application with interest rates following normal and beta distributions”. Ratio Mathematica, 28(1), pp. 15-30. doi: 10.23755/rm.v28i1.25.

Examples

# example 1
data=c(0.00,-0.05,-0.05,-0.06,-0.06,0.02,-0.06,-0.05,-0.04,-0.05,
-0.03,-0.06,0.04,-0.05,-0.08,-0.05,-0.12, -0.03,-0.05,-0.04,-0.06)
FV_pre_beta_kmom(data,8)

# example 2
data<-rnorm(n=200,m=0.075,sd=0.2)
FV_pre_beta_kmom(data,8)

Compute the final expected value of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, using the method of Mood et al.

Description

Compute the final expected value of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, using the method of Mood et al.

Usage

FV_pre_mood(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Source

Cruz Rambaud, S.; Maturo, F. and Sánchez Pérez A. M. (2017): “Expected present and final value of an annuity when some non-central moments of the capitalization factor are unknown: Theory and an application using R”. In Š. Hošková-Mayerová, et al. (Eds.), Mathematical-Statistical Models and Qualitative Theories for Economic and Social Sciences (pp. 233-248). Springer, Cham. doi:10.1007/978-3-319-54819-7_16.

Examples

#example 1
data=c(0.298,0.255,0.212,0.180,0.165,0.163,0.167,0.161,0.154,
0.128,0.079,0.059,0.042,-0.008,-0.012,-0.002)
FV_pre_mood(data,6)

# example 2
data<-rnorm(n=30,m=0.03,sd=0.01)
FV_pre_mood(data,10)

Compute the final expected value of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, using the estimated moments of the normal distribution.

Description

Compute the final expected value of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, using the estimated moments of the normal distribution.

Usage

FV_pre_norm_kmom(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Source

Cruz Rambaud, S.; Maturo, F. and Sánchez Pérez A. M. (2015): “Approach of the value of an annuity when non-central moments of the capitalization factor are known: an R application with interest rates following normal and beta distributions”. Ratio Mathematica, 28(1), pp. 15-30. doi: 10.23755/rm.v28i1.25.

Examples

# example 1
data<-rnorm(n=30,m=0.03,sd=0.01)
norm_test_jb(data) #test data
FV_pre_norm_kmom(data,8)

# example 1
data<-rnorm(n=200,m=0.075,sd=0.2)
norm_test_jb(data) #test data
FV_pre_norm_kmom(data,8)

Compute the final expected value of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, using the quadratic discount method.

Description

Compute the final expected value of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, using the quadratic discount method.

Usage

FV_pre_quad(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Source

Cruz Rambaud, S.; Maturo, F. and Sánchez Pérez A. M. (2017): “Expected present and final value of an annuity when some non-central moments of the capitalization factor are unknown: Theory and an application using R”. In Š. Hošková-Mayerová, et al. (Eds.), Mathematical-Statistical Models and Qualitative Theories for Economic and Social Sciences (pp. 233-248). Springer, Cham. doi:10.1007/978-3-319-54819-7_16.

Examples

#example 1
data=c(0.298,0.255,0.212,0.180,0.165,0.163,0.167,0.161,0.154,
0.128,0.079,0.059,0.042,-0.008,-0.012,-0.002)
FV_pre_quad(data,6)

# example 2
data<-rnorm(n=30,m=0.03,sd=0.01)
FV_pre_quad(data,10)

Compute present expected value of an n-payment annuity, with payments of 1 unit each, made at the end of every year (annuity-immediate), valued at the rate X, using the tetraparametric function approach.

Description

Compute present expected value of an n-payment annuity, with payments of 1 unit each, made at the end of every year (annuity-immediate), valued at the rate X, using the tetraparametric function approach.

Usage

PV_post_artan(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Source

Cruz Rambaud, S.; Maturo, F. and Sánchez Pérez A. M. (2017): “Expected present and final value of an annuity when some non-central moments of the capitalization factor are unknown: Theory and an application using R”. In Š. Hošková-Mayerová, et al. (Eds.), Mathematical-Statistical Models and Qualitative Theories for Economic and Social Sciences (pp. 233-248). Springer, Cham. doi:10.1007/978-3-319-54819-7_16.

Examples

#example 1
data=c(0.298,0.255,0.212,0.180,0.165,0.163,0.167,0.161,0.154,
0.128,0.079,0.059,0.042,-0.008,-0.012,-0.002)
PV_post_artan(data)

# example 2
data<-rnorm(n=30,m=0.03,sd=0.01)
PV_post_artan(data)

# example 3
data<-rnorm(n=30,m=0.03,sd=0.2)
PV_post_artan(data)

Compute the present expected value of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-due), valued at the rate X, using the cubic discount method.

Description

Compute the present expected value of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-due), valued at the rate X, using the cubic discount method.

Usage

PV_post_cubic(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

#example 1
data=c(0.298,0.255,0.212,0.180,0.165,0.163,0.167,0.161,0.154,
0.128,0.079,0.059,0.042,-0.008,-0.012,-0.002)
PV_post_cubic(data)

#example 2
data<-rnorm(n=30,m=0.03,sd=0.01)
PV_post_cubic(data)

# example 3
data = c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
data=data/100
PV_post_cubic(data)

Computes the present value of an annuity-immediate considering only non-central moments of negative orders.

Description

Computes the present value of an annuity-immediate considering only non-central moments of negative orders.

Usage

PV_post_exact(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

# example 1
data=c(0.0177, 0.0185, 0.0185, 0.0184, 0.0184, 0.0183, 0.0185, 0.0185, 0.0188, 0.0185, 
0.0180, 0.0184, 0.0191, 0.0185, 0.0184, 0.0185, 0.0186, 0.0185, 0.0188, 0.0186)
PV_post_exact(data,10)

Compute the present expected value of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, with the method of Mood et al. using some negative moments of the distribution.

Description

Compute the present expected value of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, with the method of Mood et al. using some negative moments of the distribution.

Usage

PV_post_mood_nm(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Source

Mood, A. M.; Graybill, F. A. and Boes, D. C. (1974). Introduction to the Theory of Statistics (3rd Ed.). New York: McGraw Hill.

Rice, J. A. (1995). Mathematical Statistics and Data Analysis (2nd Ed.). California: Ed. Duxbury Press.

Examples

#example 1
data=c(0.298,0.255,0.212,0.180,0.165,0.163,0.167,0.161,0.154,
0.128,0.079,0.059,0.042,-0.008,-0.012,-0.002)
PV_post_mood_nm(data)

# example 2
data<-rnorm(n=30,m=0.03,sd=0.01)
PV_post_mood_nm(data)

# example 3
data = c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
data=data/100
PV_post_mood_nm(data)

Compute the present expected value of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, with the method of Mood et al. using some positive moments of the distribution.

Description

Compute the present expected value of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, with the method of Mood et al. using some positive moments of the distribution.

Usage

PV_post_mood_pm(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Source

Mood, A. M.; Graybill, F. A. and Boes, D. C. (1974). Introduction to the Theory of Statistics (3rd Ed.). New York: McGraw Hill.

Rice, J. A. (1995). Mathematical Statistics and Data Analysis (2nd Ed.). California: Ed. Duxbury Press.

Cruz Rambaud, S.; Maturo, F. and Sánchez Pérez A. M. (2017): “Expected present and final value of an annuity when some non-central moments of the capitalization factor are unknown: Theory and an application using R”. In Š. Hošková-Mayerová, et al. (Eds.), Mathematical-Statistical Models and Qualitative Theories for Economic and Social Sciences (pp. 233-248). Springer, Cham. doi:10.1007/978-3-319-54819-7_16.

Examples

#example 1
data=c(0.298,0.255,0.212,0.180,0.165,0.163,0.167,0.161,0.154,
0.128,0.079,0.059,0.042,-0.008,-0.012,-0.002)
PV_post_mood_pm(data)

# example 2
data<-rnorm(n=30,m=0.03,sd=0.01)
PV_post_mood_pm(data)

# example 3
data = c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
data=data/100
PV_post_mood_pm(data)

Compute the present value of an annuity-immediate considering only non-central moments of negative orders. The calculation is performed by using the function triangular\_moments\_3 for the moments greater than -2 (in absolute value).

Description

Compute the present value of an annuity-immediate considering only non-central moments of negative orders. The calculation is performed by using the function triangular\_moments\_3 for the moments greater than -2 (in absolute value).

Usage

PV_post_triang_3(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

data=c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
PV_pre_triang_3(data,10)

Compute the present value of an annuity-immediate considering only non-central moments of negative orders. The calculation is performed by using the moments of the fitted triangular distribution of the random variable "capitalization factor" U (which are obtained from the definition of negative moment of a continuous random variable).

Description

Compute the present value of an annuity-immediate considering only non-central moments of negative orders. The calculation is performed by using the moments of the fitted triangular distribution of the random variable "capitalization factor" U (which are obtained from the definition of negative moment of a continuous random variable).

Usage

PV_post_triang_dis(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

data=c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
PV_post_triang_dis(data,10)

Compute the present expected value of an n-payment annuity, with payments of 1 unit each, made at the beginning of every year (annuity-due), valued at the rate X, using the tetraparametric function approach.

Description

Compute the present expected value of an n-payment annuity, with payments of 1 unit each, made at the beginning of every year (annuity-due), valued at the rate X, using the tetraparametric function approach.

Usage

PV_pre_artan(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Source

Cruz Rambaud, S.; Maturo, F. and Sánchez Pérez A. M. (2017): “Expected present and final value of an annuity when some non-central moments of the capitalization factor are unknown: Theory and an application using R”. In Š. Hošková-Mayerová, et al. (Eds.), Mathematical-Statistical Models and Qualitative Theories for Economic and Social Sciences (pp. 233-248). Springer, Cham. doi:10.1007/978-3-319-54819-7_16.

Examples

#example 1
data=c(0.298,0.255,0.212,0.180,0.165,0.163,0.167,0.161,0.154,0.128,
0.079,0.059,0.042,-0.008,-0.012,-0.002)
PV_pre_artan(data)

# example 2
data<-rnorm(n=30,m=0.03,sd=0.01)
PV_pre_artan(data)

Compute the present expected value of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, using the cubic discount method.

Description

Compute the present expected value of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, using the cubic discount method.

Usage

PV_pre_cubic(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

#example 1
data=c(0.298,0.255,0.212,0.180,0.165,0.163,0.167,0.161,0.154,
0.128,0.079,0.059,0.042,-0.008,-0.012,-0.002)
PV_pre_cubic(data)

#example 2
data<-rnorm(n=30,m=0.03,sd=0.01)
PV_pre_cubic(data)

# example 3
data = c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
data=data/100
PV_pre_cubic(data)

Compute the present value of an annuity-due considering only non-central moments of negative orders.

Description

Compute the present value of an annuity-due considering only non-central moments of negative orders.

Usage

PV_pre_exact(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

# example 1
data=c(0.0177, 0.0185, 0.0185, 0.0184, 0.0184, 0.0183, 0.0185, 0.0185, 0.0188, 
0.0185, 0.0180, 0.0184, 0.0191, 0.0185, 0.0184, 0.0185, 0.0186, 0.0185, 0.0188, 0.0186)
PV_pre_exact(data,10)

Compute the present expected value of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, with the method of Mood et al. using some negative moments of the distribution.

Description

Compute the present expected value of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, with the method of Mood et al. using some negative moments of the distribution.

Usage

PV_pre_mood_nm(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

#example 1
data=c(0.298,0.255,0.212,0.180,0.165,0.163,0.167,0.161,0.154,
0.128,0.079,0.059,0.042,-0.008,-0.012,-0.002)
PV_pre_mood_nm(data)

# example 2
data<-rnorm(n=30,m=0.03,sd=0.01)
PV_pre_mood_nm(data)

# example 3
data = c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,
1.84,1.85,1.86,1.85,1.88,1.86)
data=data/100
PV_pre_mood_nm(data)

Compute the present expected value of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, with the method of Mood et al. using some positive moments of the distribution.

Description

Compute the present expected value of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, with the method of Mood et al. using some positive moments of the distribution.

Usage

PV_pre_mood_pm(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Source

Cruz Rambaud, S.; Maturo, F. and Sánchez Pérez A. M. (2017): “Expected present and final value of an annuity when some non-central moments of the capitalization factor are unknown: Theory and an application using R”. In Š. Hošková-Mayerová, et al. (Eds.), Mathematical-Statistical Models and Qualitative Theories for Economic and Social Sciences (pp. 233-248). Springer, Cham. doi:10.1007/978-3-319-54819-7_16.

Examples

#example 1
data=c(0.298,0.255,0.212,0.180,0.165,0.163,0.167,0.161,0.154,
0.128,0.079,0.059,0.042,-0.008,-0.012,-0.002)
PV_pre_mood_pm(data)

# example 2
data<-rnorm(n=30,m=0.3,sd=0.01)
PV_pre_mood_pm(data)

# example 3
data = c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
data=data/100
PV_pre_mood_pm(data)

Compute the present value of an annuity-due considering only non-central moments of negative orders. The calculation is performed by using the function $triangular\_moments\_3$ for the moments greater than -2 (in absolute value).

Description

Compute the present value of an annuity-due considering only non-central moments of negative orders. The calculation is performed by using the function $triangular\_moments\_3$ for the moments greater than -2 (in absolute value).

Usage

PV_pre_triang_3(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

data=c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
PV_pre_triang_3(data,10)

Compute the present value of an annuity-due considering only non-central moments of negative orders. The calculation is performed by using the moments of the fitted triangular distribution of the random variable "capitalization factor" U (which are obtained from the definition of negative moment of a continuous random variable)

Description

Compute the present value of an annuity-due considering only non-central moments of negative orders. The calculation is performed by using the moments of the fitted triangular distribution of the random variable "capitalization factor" U (which are obtained from the definition of negative moment of a continuous random variable)

Usage

PV_pre_triang_dis(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

data=c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
PV_pre_triang_dis(data,10)

Compute the parameters of the beta distribution and plot normalized data.

Description

Compute the parameters of the beta distribution and plot normalized data.

Usage

beta_parameters(data)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Source

Cruz Rambaud, S.; Maturo, F. and Sánchez Pérez A. M. (2015): "Approach of the value of an annuity when non-central moments of the capitalization factor are known: an R application with interest rates following normal and beta distributions". Ratio Mathematica, 28(1), pp. 15-30. doi: 10.23755/rm.v28i1.25.

Examples

# example 1
data=c(0.00,-0.05,-0.05,-0.06,-0.06,0.02,-0.06,-0.05,-0.04,-0.05,
-0.03,-0.06,0.04,-0.05,-0.08,-0.05,-0.12,-0.03,-0.05,-0.04,-0.06)
beta_parameters(data)

# example 2
data<-rnorm(n=200,m=0.075,sd=0.2)
beta_parameters(data)

Compute the exact moments of a distribution.

Description

Compute the exact moments of a distribution.

Usage

moment(x,order,central, absolute, na.rm)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Source

Cruz Rambaud, S.; Maturo, F. and Sánchez Pérez A. M. (2015): “Approach of the value of an annuity when non-central moments of the capitalization factor are known: an R application with interest rates following normal and beta distributions”. Ratio Mathematica, 28(1), pp. 15-30. doi: 10.23755/rm.v28i1.25.

Examples

#example 1
data=c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
moment(data,3)

Fit the data to a normal curve and compute the moments of the normal distribution according to the definition (as integral).

Description

Fit the data to a normal curve and compute the moments of the normal distribution according to the definition (as integral).

Usage

norm_mom(data,order)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Source

Cruz Rambaud, S.; Maturo, F. and Sánchez Pérez A. M. (2015): “Approach of the value of an annuity when non-central moments of the capitalization factor are known: an R application with interest rates following normal and beta distributions”. Ratio Mathematica, 28(1), pp. 15-30. doi: 10.23755/rm.v28i1.25.

Examples

#example 1
data=c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
data=data/100
norm_mom(data,5)

Compute the Jarque-Bera test for checking the assumption of normality of the interest rates distribution and returns the parameters of the fitted normal distribution.

Description

Compute the Jarque-Bera test for checking the assumption of normality of the interest rates distribution and returns the parameters of the fitted normal distribution.

Usage

norm_test_jb(data)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Source

Cruz Rambaud, S.; Maturo, F. and Sánchez Pérez A. M. (2015): “Approach of the value of an annuity when non-central moments of the capitalization factor are known: an R application with interest rates following normal and beta distributions”. Ratio Mathematica, 28(1), pp. 15-30. doi: 10.23755/rm.v28i1.25.

Examples

#example 1
data=c(0.298,0.255,0.212,0.180,0.165,0.163,0.167,0.161,
0.154,0.128,0.079,0.059,0.042,-0.008,-0.012,-0.002)
norm_test_jb(data)

# example 2
data<-rnorm(n=30,m=0.03,sd=0.01)
norm_test_jb(data)

# example 3
data=runif(999, min = 0, max = 1)
norm_test_jb(data)

# example 4
data=c(0.00,-0.05,-0.05,-0.06,-0.06,0.02,-0.06,-0.05,-0.04,-0.05,
-0.03,-0.06,0.04,-0.05,-0.08,-0.05,-0.12,-0.03,-0.05,-0.04,-0.06)
norm_test_jb(data)

Plot the final expected value of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, using the estimated moments of the beta distribution.

Description

Plot the final expected value of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, using the estimated moments of the beta distribution.

Usage

plot_FV_post_beta_kmom(data,years,lwd,lty)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

# example 1
data<-runif(34, 0,1)
plot_FV_post_beta_kmom(data,8)

Plot the final expected value of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, using the estimated moments of the normal distribution.

Description

Plot the final expected value of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, using the estimated moments of the normal distribution.

Usage

plot_FV_post_norm_kmom(data,years,lwd,lty)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

# example 1
data<-rnorm(n=30,m=0.03,sd=0.01)
plot_FV_post_norm_kmom(data,8)

# example 2
data<-rnorm(n=200,m=0.075,sd=0.2)
plot_FV_post_norm_kmom(data,8)

Plot the final expected value of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, using the estimated moments of the beta distribution.

Description

Plot the final expected value of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, using the estimated moments of the beta distribution.

Usage

plot_FV_pre_beta_kmom(data,years,lwd,lty)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

# example 1
data<-runif(34, 0,1)
plot_FV_pre_beta_kmom(data,8)

Plot the final expected value of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, using the estimated moments of the normal distribution.

Description

Plot the final expected value of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, using the estimated moments of the normal distribution.

Usage

plot_FV_pre_norm_kmom(data,years,lwd,lty)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

# example 1
data<-rnorm(n=30,m=0.03,sd=0.01)
plot_FV_pre_norm_kmom(data,8)


# example 2
data<-rnorm(n=200,m=0.075,sd=0.2)
plot_FV_pre_norm_kmom(data,8)

Plot the final expected values of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, using different approaches.

Description

Plot the final expected values of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, using different approaches.

Usage

plot_FVs_post(data,years,lwd,lty1,lty2,lty3)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

#example 1
data = c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
data=data/100
plot_FVs_post(data)

# example 2
data<-rnorm(n=30,m=0.03,sd=0.003)
plot_FVs_post(data)

Plot the final expected values of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, using different approaches.

Description

Plot the final expected values of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, using different approaches.

Usage

plot_FVs_pre(data,years,lwd,lty1,lty2,lty3)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

#example 1
data = c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
data=data/100
plot_FVs_pre(data)

# example 2
data<-rnorm(n=30,m=0.03,sd=0.003)
plot_FVs_pre(data)

Plot the present expected values of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, using different approaches.

Description

Plot the present expected values of an n-payment annuity, with payments of 1 unit each made at the end of every year (annuity-immediate), valued at the rate X, using different approaches.

Usage

plot_PVs_post(data,years,lwd,lty1,lty2,lty3,lty4,lty5,lty6)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

# example 1
data = c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
data=data/100
plot_PVs_post(data)

# example 2
data<-rnorm(n=30,m=0.03,sd=0.003)
plot_PVs_post(data)

Plot the present expected values of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, using different approaches.

Description

Plot the present expected values of an n-payment annuity, with payments of 1 unit each made at the beginning of every year (annuity-due), valued at the rate X, using different approaches.

Usage

plot_PVs_pre(data,years,lwd,lty1,lty2,lty3,lty4,lty5,lty6)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

# example 1
data = c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
data=data/100
plot_PVs_pre(data)

# example 2
data<-rnorm(n=30,m=0.03,sd=0.003)
plot_PVs_pre(data)

Compute the negatives moments (different from orders 1 and 2) of the fitted triangular distribution of the random variable X.

Description

Compute the negatives moments (different from orders 1 and 2) of the fitted triangular distribution of the random variable X.

Usage

triangular_moments_3(data,order)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

#example 1
data=c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
triangular_moments_3(data,3)
triangular_moments_3(data,4)

# example 2 - first 10 negative moments of fitted triangular distribution 
#(an example from normal distributed simulated data)
data<-rnorm(n=200,m=0.75,sd=0.2)
triangular_parameters(data)
first10negmoments=rep(NA,10)  #except first and second
for (i in 3:10) first10negmoments[i]=triangular_moments_3(data,i)
first10negmoments

Compute the negatives moments (different from orders 1 and 2) of the fitted triangular distribution of the random variable "capitalization factor" U.

Description

Compute the negatives moments (different from orders 1 and 2) of the fitted triangular distribution of the random variable "capitalization factor" U.

Usage

triangular_moments_3_U(data,order)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

#example 1
data=c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
triangular_moments_3_U(data,3)
triangular_moments_3_U(data,4)

# example 2 - first 10 negative moments of fitted triangular distribution 
#(an example from normal distributed simulated data)
data<-rnorm(n=200,m=0.75,sd=0.2)
triangular_parameters(data)
first10negmoments=rep(NA,10)  #except first and second
for (i in 3:10) first10negmoments[i]=triangular_moments_3_U(data,i)
first10negmoments

Compute the negative moments of the fitted triangular distribution of the random variable X according to the definition (as integral).

Description

Compute the negative moments of the fitted triangular distribution of the random variable X according to the definition (as integral).

Usage

triangular_moments_dis(data,order)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

# example 1
data=c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
triangular_moments_dis(data,1)
triangular_moments_dis(data,2)
triangular_moments_dis(data,3)
triangular_moments_dis(data,4)

# example 2 - first 10 negative moments of fitted triangular distribution 
#(an example from normal distributed simulated data)
data<-rnorm(n=200,m=0.75,sd=0.2)
triangular_parameters(data)
first10negmoments=rep(NA,10)
for (i in 1:10) first10negmoments[i]=triangular_moments_dis(data,i)
first10negmoments

Compute the negative moments of the fitted triangular distribution of the random variable "capitalization factor" U according to the definition (as integral).

Description

Compute the negative moments of the fitted triangular distribution of the random variable "capitalization factor" U according to the definition (as integral).

Usage

triangular_moments_dis_U(data,order)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

# example 1
data=c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
triangular_moments_dis_U(data,1)
triangular_moments_dis_U(data,2)
triangular_moments_dis_U(data,3)
triangular_moments_dis_U(data,4)

# example 2 - first 10 negative moments of fitted triangular distribution 
#(an example from normal distributed simulated data)
data<-rnorm(n=200,m=0.75,sd=0.2)
triangular_parameters(data)
first10negmoments=rep(NA,10)
for (i in 1:10) first10negmoments[i]=triangular_moments_dis_U(data,i)
first10negmoments

Compute the parameters and plot the fitted triangular distribution of the random variable X.

Description

Compute the parameters and plot the fitted triangular distribution of the random variable X.

Usage

triangular_parameters(data)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

# example 1
data=c(0.00,-0.05,-0.05,-0.06,-0.06,0.02,-0.06,-0.05,-0.04,-0.05,
-0.03,-0.06,0.04,-0.05,-0.08,-0.05,-0.12,-0.03,-0.05,-0.04,-0.06)
triangular_parameters(data)

# example 2
data<-rnorm(n=200,m=0.75,sd=0.2)
triangular_parameters(data)


# example 3
data = c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
triangular_parameters(data)

Return the parameters of the fitted triangular distribution of the random variable "capitalization factor" U.

Description

Return the parameters of the fitted triangular distribution of the random variable "capitalization factor" U.

Usage

triangular_parameters_U(data)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

# example 1
data = c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
triangular_parameters_U(data)

Compute the variance of the present value of an annuity using "discrete random variable" approach.

Description

Compute the variance of the present value of an annuity using "discrete random variable" approach.

Usage

variance_drv(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

# example 1
data = c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
data=data/100
variance_drv(data)

Compute the variance of the present value of an annuity-immediate using the Mood et al. approximation and some non-central moments of negative order.

Description

Compute the variance of the present value of an annuity-immediate using the Mood et al. approximation and some non-central moments of negative order.

Usage

variance_post_mood_nm(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

# example 1
data = c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
data=data/100
variance_post_mood_nm(data)

Compute the variance of the present value of an annuity-immediate using the Mood et al. approximation and some non-central moments of positive order.

Description

Compute the variance of the present value of an annuity-immediate using the Mood et al. approximation and some non-central moments of positive order.

Usage

variance_post_mood_pm(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

# example 1
data = c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
data=data/100
variance_post_mood_pm(data)

Compute the variance of the present value of an annuity-due using the Mood et al. approximation and some non-central moments of negative order.

Description

Compute the variance of the present value of an annuity-due using the Mood et al. approximation and some non-central moments of negative order.

Usage

variance_pre_mood_nm(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

# example 1
data = c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
data=data/100
variance_pre_mood_nm(data)

Compute the variance of the present value of an annuity-due using the Mood et al. approximation and some non-central moments of positive order.

Description

Compute the variance of the present value of an annuity-due using the Mood et al. approximation and some non-central moments of positive order.

Usage

variance_pre_mood_pm(data,years)

Arguments

Author(s)

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez Pérez

Examples

# example 1
data = c(1.77,1.85,1.85,1.84,1.84,1.83,1.85,1.85,1.88,1.85,1.80,1.84,1.91,1.85,1.84,1.85,
1.86,1.85,1.88,1.86)
data=data/100
variance_pre_mood_pm(data)