Univariate Proability Distributions with Truncation

Description

Truncation of univariate probability distributions. The probability distribution can come from other packages so long as the function names follow the standard d, p, q, r naming format. Also other univariate probability distributions are included.

Author(s)

Maintainer: Jared Studyvin studyvinstat@gmail.com

Log-Logistic Distribution

Description

The probability density function, cumulative density function, inverse cumulative density function, random generation for the log logistic distribution.

Usage

dllog(x, shape = 1, scale = 1, log = FALSE, ...)

llogSummaryStats(shape, scale, ...)

pllog(q, shape = 1, scale = 1, lower.tail = TRUE, log.p = FALSE, ...)

qllog(p, shape = 1, scale = 1, lower.tail = TRUE, log.p = FALSE, ...)

rllog(n, shape = 1, scale = 1, ...)

Arguments

Details

If X is a random variable distributed according to a logistic distribution, then Y = exp(X) has a log-logistic distribution.

The log-logistic distribution with parameters shape = a and scale = s has density

f(x) = \frac{(\frac{1}{a*exp(s))})(\frac{x}{\exp{s}})^{\frac{1}{a} - 1}}{(1+(\frac{x}{\exp{s}})^{1/a})^2}

for x >= 0, a > 1, and s > 0.

The median is exp(s), mean is

\frac{a\pi*exp(s)}{sin(a*\pi)}

for 1/a > 1. The variance is

(exp(s))^2(\frac{2*\pi*a}{(sin(2*pi*a))}- \frac{(a*\pi)^2}{(sin^2(a*\pi))})

for 1/a > 2. The mode is

exp(s)(\frac{(1/a) - 1}{(1/a) + 1})^{a}

for 1/a > 1 otherwise it is zero.

Value

dllog returns vector of the densities.

llogSummaryStats returns a data frame of summary statistics.

pllog returns a vector of probabilities.

qllog returns a vector of quantiles.

rllog returns a vector of random log-logistic variates.

See Also

Logistic

Examples

y <- rllog(5,shape=1,scale=1/3)
dllog(x=y,shape=1,scale=1/3)
dlogis(x=log(y),location=1/3,scale=1)/y

pllog(q=y,shape=1,scale=1/3)
qllog(p=seq(0,1,by=.25),shape=1,scale=1/3)

Get Distribution Functions

Description

Determines if the distribution functions are available. This is intended for internal use only.

Usage

getDistributionFunction(type, distr, ...)

Arguments

Details

It is determined that paste0(type, dist) is a function and returns that function. The nature of the returned function is not verified.

Value

Function, the first function in the search path that matches the name paste0(type, dist).

Examples

fun <- getDistributionFunction(type="q",distr="norm")

Truncated Distributions

Description

Truncated probability density function, truncated cumulative density function, inverse truncated cumulative density function, and random variates from a truncated distribution.

Usage

dtrunc(x, distr, ..., low = -Inf, high = Inf, log = FALSE)

ptrunc(q, distr, ..., low = -Inf, high = Inf, lower.tail = TRUE, log.p = FALSE)

qtrunc(p, distr, ..., low = -Inf, high = Inf, lower.tail = TRUE, log.p = FALSE)

rtrunc(n, distr, ..., low = -Inf, high = Inf)

Arguments

Details

The non truncated distribution functions are assumed to be available. For example if the normal distribution is desired then used distr='norm', the functions then look for 'qnorm', 'pnorm', etc.

The truncation interval is (low, high], which only matters for discrete distribution.

The random variates are produced using the direct method (see Casella and Berger 2002).

Value

dtrunc returns a vector of densities.

ptrunc returns a vector of probabilities.

qtrunc returns a vector of quantiles.

rtrunc returns a vector of random variates.

References

G. Casella and R. L. Berger. Statistical inference. Vol. 2. Duxbury Pacific Grove, CA, 2002.

Examples

## dtrunc
# not truncted
dnorm(5,mean=5)
dtrunc(x=5,distr='norm',mean=5)
# truncated
dtrunc(x=5,distr='norm',mean=5,low=4, high=5.5)



## ptrunc
#not truncated
pgamma(2, shape=3, rate=2)
ptrunc(2, distr = 'gamma', shape=3, rate=2)
# truncated
ptrunc(2, distr = 'gamma', shape=3, rate=2, low=1, high=5)

## upper tail
# not truncated
pgamma(2, shape=3, rate=2,lower.tail=FALSE)
ptrunc(2, distr='gamma', shape=3, rate=2, lower.tail=FALSE)
# truncated
ptrunc(2, distr='gamma', shape=3, rate=2, low=1, high=5, lower.tail=FALSE)



## qtrunc
#not truncated
qnorm(p=.975)
qtrunc(p=.975,distr='norm')
# truncted
qtrunc(p=.975,distr='norm', low=0, high=1)

## upper tail
# not truncted
qnorm(p=.975,lower.tail=FALSE)
qtrunc(p=.975, distr='norm', lower.tail=FALSE)
# truncated
qtrunc(p=.975, distr='norm', low=0, high=1, lower.tail=FALSE)

## rtrunc
rtrunc(n=5, distr = 'gamma', shape=3, rate=2, low=2, high=5)