Test the shape1 parameter of a beta distribution.

Description

Test the shape1 parameter of a beta distribution.

Usage

beta_shape1_one_sample(x, shape1, alternative = "two.sided", conf.level = 0.95)

Arguments

Value

An S3 class containing the test statistic, p value, likelihood based confidence interval, and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rbeta(100, shape1 = 1, shape2 = 2)
beta_shape1_one_sample(x, 1, "two.sided")

# Null is false
set.seed(1)
x <- rbeta(100, shape1 = 3, shape2 = 2)
beta_shape1_one_sample(x, 1, "greater")

Test the equality of shape 1 parameters of beta distributions.

Description

Test the equality of shape 1 parameters of beta distributions.

Usage

beta_shape1_one_way(x, fctr, conf.level = 0.95)

Arguments

Details

• Null: All shape1s are equal. (shape1_1 = shape1_2 ... shape1_k).

• Alternative: At least one shape1 is not equal.

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rbeta(150, 1, 2)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
beta_shape1_one_way(x, fctr, .95)

# Null is false
set.seed(1)
x <- c(rbeta(50, 1, 2), rbeta(50, 2, 2), rbeta(50, 3, 2))
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
beta_shape1_one_way(x, fctr, .95)

Test the shape2 parameter of a beta distribution.

Description

Test the shape2 parameter of a beta distribution.

Usage

beta_shape2_one_sample(x, shape2, alternative = "two.sided", conf.level = 0.95)

Arguments

Value

An S3 class containing the test statistic, p value, likelihood based confidence interval, and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rbeta(100, shape1 = 1, shape2 = 1)
beta_shape2_one_sample(x, 1, "two.sided")

# Null is false
set.seed(1)
x <- rbeta(100, shape1 = 1, shape2 = 3)
beta_shape2_one_sample(x, 1, "greater")

Test the equality of shape 2 parameters of beta distributions.

Description

Test the equality of shape 2 parameters of beta distributions.

Usage

beta_shape2_one_way(x, fctr, conf.level = 0.95)

Arguments

Details

• Null: All shape2s are equal. (shape2_1 = shape2_2 ... shape2_k).

• Alternative: At least one shape2 is not equal.

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rbeta(150, 2, 2)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
beta_shape2_one_way(x, fctr, .95)

# Null is false
set.seed(1)
x <- c(rbeta(50, 2, 1), rbeta(50, 2, 2), rbeta(50, 2, 3))
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
beta_shape2_one_way(x, fctr, .95)

Test the p parameter of a binomial distribution.

Description

Test the p parameter of a binomial distribution.

Usage

binomial_p_one_sample(x, n, p, alternative = "two.sided", conf.level = 0.95)

Arguments

Value

An S3 class containing the test statistic, p value, likelihood based confidence interval, and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true. 52 successes. 100 trials
binomial_p_one_sample(52, 100, .50, "two.sided")

# Null is false. 75 successes. 100 trials
binomial_p_one_sample(75, 100, .50, "two.sided")

Test the equality of p parameters of binomial distributions.

Description

Test the equality of p parameters of binomial distributions.

Usage

binomial_p_one_way(x, n, fctr, conf.level = 0.95)

Arguments

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true.
set.seed(1)
x <- rbinom(3, 50, .5)
n <- rep(50, length(x))
fctr <- factor(1:length(x))
binomial_p_one_way(x, n, fctr, .95)

# Null is false
set.seed(1)
x <- rbinom(3, 50, c(.25, .50, .75))
n <- rep(50, length(x))
fctr <- factor(1:length(x))
binomial_p_one_way(x, n, fctr, .95)

Test the location parameter of a cauchy distribution.

Description

Test the location parameter of a cauchy distribution.

Usage

cauchy_location_one_sample(
  x,
  location,
  alternative = "two.sided",
  conf.level = 0.95
)

Arguments

Value

An S3 class containing the test statistic, p value, likelihood based confidence interval, and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rcauchy(n = 100, location = 1, scale = 2)
cauchy_location_one_sample(x, 1, "two.sided")

# Null is false
set.seed(1)
x <- rcauchy(n = 100, location = 3, scale = 2)
cauchy_location_one_sample(x, 1, "greater")

Test the equality of location parameters of cauchy distributions.

Description

Test the equality of location parameters of cauchy distributions.

Usage

cauchy_location_one_way(x, fctr, conf.level = 0.95)

Arguments

Details

• All locations are equal. (location_1 = location_2 ... location_k).

• Alternative: At least one location is not equal.

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rcauchy(n = 150, location = 1, scale = 2)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
cauchy_location_one_way(x, fctr, .95)

# Null is false
set.seed(1)
x <- c(rcauchy(50, 1, 2), rcauchy(50, 2, 2), rcauchy(50, 3, 2))
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
cauchy_location_one_way(x, fctr, .95)

Test the scale parameter of a cauchy distribution.

Description

Test the scale parameter of a cauchy distribution.

Usage

cauchy_scale_one_sample(x, scale, alternative = "two.sided", conf.level = 0.95)

Arguments

Value

An S3 class containing the test statistic, p value, likelihood based confidence interval, and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rcauchy(n = 100, location = 1, scale = 2)
cauchy_scale_one_sample(x, 2, "two.sided")

# Null is false
set.seed(1)
x <- rcauchy(n = 100, location = 3, scale = 2)
cauchy_scale_one_sample(x, 1, "greater")

Test the equality of scale parameters of cauchy distributions.

Description

Test the equality of scale parameters of cauchy distributions.

Usage

cauchy_scale_one_way(x, fctr, conf.level = 0.95)

Arguments

Details

• Null: All scales are equal. (scale_1 = scale_2 ... scale_k).

• Alternative: At least one scale is not equal.

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rcauchy(n = 150, 1, 2)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
cauchy_scale_one_way(x, fctr, .95)

# Null is false
set.seed(1)
x <- c(rcauchy(50, 2, 1), rcauchy(50, 2, 2), rcauchy(50, 2, 3))
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
cauchy_scale_one_way(x, fctr, .95)

Test the mean parameter of an unknown distribution.

Description

Test the mean parameter of an unknown distribution.

Usage

empirical_mu_one_sample(x, mu, alternative = "two.sided", conf.level = 0.95)

Arguments

Value

An S3 class containing the test statistic, p value, likelihood based confidence interval, and alternative hypothesis.

Source

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Owen. Empirical Likelihood. Chapman & Hall/CRC.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rnorm(25, 0, 1)
empirical_mu_one_sample(x, 0, "two.sided")

# Null is false
set.seed(1)
x <- rnorm(25, 2, 1)
empirical_mu_one_sample(x, 1, "greater")

Test the equality of means of an unknown distribution.

Description

Test the equality of means of an unknown distribution.

Usage

empirical_mu_one_way(x, fctr, conf.level = 0.95)

Arguments

Details

• Null: All mus are equal. (mu1 = mu2 ... muk).

• Alternative: At least one mu is not equal.

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Owen. Empirical Likelihood. Chapman & Hall/CRC.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rnorm(75, 1, 1)
fctr <- c(rep(1, 25), rep(2, 25), rep(3, 25))
fctr <- factor(fctr, levels = c("1", "2", "3"))
empirical_mu_one_way(x, fctr, .95)

# Null is false
set.seed(1)
x <- c(rnorm(25, 1, 1), rnorm(25, 2, 1), rnorm(25, 3, 1))
fctr <- c(rep(1, 25), rep(2, 25), rep(3, 25))
fctr <- factor(fctr, levels = c("1", "2", "3"))
empirical_mu_one_way(x, fctr, .95)

Test a quantile of an unknown distribution.

Description

Test a quantile of an unknown distribution.

Usage

empirical_quantile_one_sample(
  x,
  Q,
  value,
  alternative = "two.sided",
  conf.level = 0.95
)

Arguments

Details

For confidence intervals, an endpoint may be outside the observed range of x. In this case, NA is returned. Reducing confidence or collecting more data will make the CI computable.

Value

An S3 class containing the test statistic, p value, likelihood based confidence interval, and alternative hypothesis.

Source

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Owen. Empirical Likelihood. Chapman & Hall/CRC.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rnorm(25, 0, 1)
empirical_quantile_one_sample(x, .5, 0, "two.sided")

# Null is false
set.seed(1)
x <- rnorm(25, 2, 1)
empirical_quantile_one_sample(x, .5, 1, "greater")

Test the equality of a quantile from an unknown distribution.

Description

Test the equality of a quantile from an unknown distribution.

Usage

empirical_quantile_one_way(x, Q, fctr, conf.level = 0.95)

Arguments

Details

• Null: Quantiles are equal. (Q1 = Q2 ... Qk).

• Alternative: At least one quantile is not equal.

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Owen. Empirical Likelihood. Chapman & Hall/CRC.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rnorm(75, 1, 1)
fctr <- c(rep(1, 25), rep(2, 25), rep(3, 25))
fctr <- factor(fctr, levels = c("1", "2", "3"))
empirical_quantile_one_way(x, .50, fctr, .95)

# Null is false
set.seed(1)
x <- c(rnorm(25, 1, 1), rnorm(25, 2, 1), rnorm(25, 3, 1))
fctr <- c(rep(1, 25), rep(2, 25), rep(3, 25))
fctr <- factor(fctr, levels = c("1", "2", "3"))
empirical_quantile_one_way(x, .50, fctr, .95)

Test the rate parameter of a exponential distribution.

Description

Test the rate parameter of a exponential distribution.

Usage

exponential_rate_one_sample(
  x,
  rate,
  alternative = "two.sided",
  conf.level = 0.95
)

Arguments

Value

An S3 class containing the test statistic, p value, likelihood based confidence interval, and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rexp(100, 1)
exponential_rate_one_sample(x, 1, "two.sided")

# Null is false
set.seed(1)
x <- rexp(100, 3)
exponential_rate_one_sample(x, 1, "greater")

Test the equality of rate parameters of exponential distributions.

Description

Test the equality of rate parameters of exponential distributions.

Usage

exponential_rate_one_way(x, fctr, conf.level = 0.95)

Arguments

Details

• Null: All lambdas are equal. (lambda_1 = lambda_2 ... lambda_k).

• Alternative: At least one lambda is not equal.

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rexp(150, 1)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
exponential_rate_one_way(x, fctr, .95)

# Null is false
set.seed(1)
x <- c(rexp(50, 1), rexp(50, 2), rexp(50, 3))
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
exponential_rate_one_way(x, fctr, .95)

Test the rate parameter of a gamma distribution.

Description

Test the rate parameter of a gamma distribution.

Usage

gamma_rate_one_sample(x, rate, alternative = "two.sided", conf.level = 0.95)

Arguments

Value

An S3 class containing the test statistic, p value, likelihood based confidence interval, and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rgamma(100, shape = 1, rate = 1)
gamma_rate_one_sample(x, 1, "two.sided")

# Null is false
set.seed(1)
x <- rgamma(100, shape = 1, rate = 2)
gamma_rate_one_sample(x, 1, "greater")

Test the equality of rate parameters of gamma distributions.

Description

Test the equality of rate parameters of gamma distributions.

Usage

gamma_rate_one_way(x, fctr, conf.level = 0.95)

Arguments

Details

• Null: All rates are equal. (rate_1 = rate_2 ... rate_k).

• Alternative: At least one rate is not equal.

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rgamma(150, 1, 2)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
gamma_rate_one_way(x, fctr, .95)

# Null is false
set.seed(1)
x <- c(rgamma(50, 2, 1), rgamma(50, 2, 2), rgamma(50, 2, 3))
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
gamma_rate_one_way(x, fctr, .95)

Test the scale parameter of a gamma distribution.

Description

Test the scale parameter of a gamma distribution.

Usage

gamma_scale_one_sample(x, scale, alternative = "two.sided", conf.level = 0.95)

Arguments

Value

An S3 class containing the test statistic, p value, likelihood based confidence interval, and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rgamma(100, shape = 1, scale = 2)
gamma_scale_one_sample(x, 2, "two.sided")

# Null is false
set.seed(1)
x <- rgamma(100, shape = 1, scale = 2)
gamma_scale_one_sample(x, 1, "greater")

Test the equality of scale parameters of gamma distributions.

Description

Test the equality of scale parameters of gamma distributions.

Usage

gamma_scale_one_way(x, fctr, conf.level = 0.95)

Arguments

Details

• Null: Null: All scales are equal. (scale_1 = scale_2 ... scale_k).

• Alternative: At least one scale is not equal.

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rgamma(150, 1, scale = 2)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
gamma_scale_one_way(x, fctr, .95)

# Null is false
set.seed(1)
x <- c(rgamma(50, 2, scale = 1), rgamma(50, 2, scale = 2), rgamma(50, 2, scale = 3))
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
gamma_scale_one_way(x, fctr, .95)

Test the shape parameter of a gamma distribution.

Description

Test the shape parameter of a gamma distribution.

Usage

gamma_shape_one_sample(x, shape, alternative = "two.sided", conf.level = 0.95)

Arguments

Value

An S3 class containing the test statistic, p value, likelihood based confidence interval, and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rgamma(100, shape = 1, scale = 2)
gamma_shape_one_sample(x, 1, "two.sided")

# Null is false
set.seed(1)
x <- rgamma(100, shape = 3, scale = 2)
gamma_shape_one_sample(x, 1, "greater")

Test the equality of shape parameters of gamma distributions.

Description

Test the equality of shape parameters of gamma distributions.

Usage

gamma_shape_one_way(x, fctr, conf.level = 0.95)

Arguments

Details

• Null: All shapes are equal. (shape_1 = shape_2 ... shape_k).

• Alternative: At least one shape is not equal.

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rgamma(150, 2, 2)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
gamma_shape_one_way(x, fctr, .95)

# Null is false
set.seed(1)
x <- c(rgamma(50, 1, 2), rgamma(50, 2, 2), rgamma(50, 3, 2))
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
gamma_shape_one_way(x, fctr, .95)

Test the mean of a gaussian distribution.

Description

Test the mean of a gaussian distribution.

Usage

gaussian_mu_one_sample(x, mu, alternative = "two.sided", conf.level = 0.95)

Arguments

Value

An S3 class containing the test statistic, p value, likelihood based confidence interval, and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rnorm(100, 0, 1)
gaussian_mu_one_sample(x, 0, "two.sided")

# Null is false
set.seed(1)
x <- rnorm(100, 3, 1)
gaussian_mu_one_sample(x, 0, "greater")

Test the equality of means of gaussian distributions.

Description

Test the equality of means of gaussian distributions.

Usage

gaussian_mu_one_way(x, fctr, conf.level = 0.95)

Arguments

Details

• Null: All mus are equal. (mu1 = mu2 ... muk).

• Alternative: At least one mu is not equal.

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rnorm(150, 1, 1)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
gaussian_mu_one_way(x, fctr, .95)

# Null is false
set.seed(1)
x <- c(rnorm(50, 1, 1), rnorm(50, 2, 1), rnorm(50, 3, 1))
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
gaussian_mu_one_way(x, fctr, .95)

Test the variance of a gaussian distribution.

Description

Test the variance of a gaussian distribution.

Usage

gaussian_variance_one_sample(
  x,
  sigma.squared,
  alternative = "two.sided",
  conf.level = 0.95
)

Arguments

Value

An S3 class containing the test statistic, p value, likelihood based confidence interval, and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rnorm(100, 0, 1)
gaussian_variance_one_sample(x, 1, "two.sided")

# Null is false
set.seed(1)
x <- rnorm(100, 0, 2)
gaussian_variance_one_sample(x, 1, "greater")

Test the equality of variance parameters of gaussian distributions.

Description

Test the equality of variance parameters of gaussian distributions.

Usage

gaussian_variance_one_way(x, fctr, conf.level = 0.95)

Arguments

Details

• Null: All variances are equal. (o^2_1 = o^2_2 ... o^2_k).

• Alternative: At least one variance is not equal.

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rnorm(150, 1, 1)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
gaussian_variance_one_way(x, fctr, .95)

# Null is false
set.seed(1)
x <- c(rnorm(50, 1, 1), rnorm(50, 1, 2), rnorm(50, 1, 3))
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
gaussian_variance_one_way(x, fctr, .95)

Test the dispersion parameter of an inverse gaussian distribution.

Description

Test the dispersion parameter of an inverse gaussian distribution.

Usage

inverse_gaussian_dispersion_one_sample(
  x,
  dispersion,
  alternative = "two.sided",
  conf.level = 0.95
)

Arguments

Value

An S3 class containing the test statistic, p value, likelihood based confidence interval, and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)
library(statmod)

# Null is true
set.seed(1)
x <- rinvgauss(n = 100, mean = 1, dispersion = 2)
inverse_gaussian_dispersion_one_sample(x, 2, "two.sided")

# Null is false
set.seed(1)
x <- rinvgauss(n = 100, mean = 1, dispersion = 2)
inverse_gaussian_dispersion_one_sample(x, 1, "greater")

Test the equality of dispersion parameters of inverse gaussian distributions.

Description

Test the equality of dispersion parameters of inverse gaussian distributions.

Usage

inverse_gaussian_dispersion_one_way(x, fctr, conf.level = 0.95)

Arguments

Details

• Null: Null: All dispersion parameters are equal. (dispersion_1 = dispersion_2 ... dispersion_k).

• Alternative: At least one dispersion is not equal.

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)
library(statmod)

# Null is true
set.seed(1)
x <- rinvgauss(n = 150, mean = 1, dispersion = 2)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
inverse_gaussian_dispersion_one_way(x, fctr, .95)

# Null is false
set.seed(1)
x <- c(
  rinvgauss(n = 50, mean = 1, dispersion = 1),
  rinvgauss(n = 50, mean = 1, dispersion = 3),
  rinvgauss(n = 50, mean = 1, dispersion = 4)
)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
inverse_gaussian_dispersion_one_way(x, fctr, .95)

Test the mean of an inverse gaussian distribution.

Description

Test the mean of an inverse gaussian distribution.

Usage

inverse_gaussian_mu_one_sample(
  x,
  mu,
  alternative = "two.sided",
  conf.level = 0.95
)

Arguments

Value

An S3 class containing the test statistic, p value, likelihood based confidence interval, and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)
library(statmod)

# Null is true
set.seed(1)
x <- rinvgauss(n = 100, mean = 1, shape = 2)
inverse_gaussian_mu_one_sample(x, 1, "two.sided")

# Null is false
set.seed(1)
x <- rinvgauss(n = 100, mean = 3, shape = 2)
inverse_gaussian_mu_one_sample(x, 1, "greater")

Test the equality of means of inverse gaussian distributions.

Description

Test the equality of means of inverse gaussian distributions.

Usage

inverse_gaussian_mu_one_way(x, fctr, conf.level = 0.95)

Arguments

Details

• Null: All mus are equal. (mu1 = mu2 ... muk).

• Alternative: At least one mu is not equal.

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)
library(statmod)

# Null is true
set.seed(1)
x <- rinvgauss(n = 150, mean = 1, shape = 2)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
inverse_gaussian_mu_one_way(x, fctr, .95)

# Null is false
set.seed(1)
x <- c(
  rinvgauss(n = 50, mean = 1, shape = 2),
  rinvgauss(n = 50, mean = 2, shape = 2),
  rinvgauss(n = 50, mean = 3, shape = 2)
)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
inverse_gaussian_mu_one_way(x, fctr, .95)

Test the shape parameter of an inverse gaussian distribution.

Description

Test the shape parameter of an inverse gaussian distribution.

Usage

inverse_gaussian_shape_one_sample(
  x,
  shape,
  alternative = "two.sided",
  conf.level = 0.95
)

Arguments

Value

An S3 class containing the test statistic, p value, likelihood based confidence interval, and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)
library(statmod)

# Null is true
set.seed(1)
x <- rinvgauss(n = 100, mean = 1, shape = 2)
inverse_gaussian_shape_one_sample(x, 2, "two.sided")

# Null is false
set.seed(1)
x <- rinvgauss(n = 100, mean = 1, shape = 2)
inverse_gaussian_shape_one_sample(x, 1, "greater")

Test the equality of shape parameters of inverse gaussian distributions.

Description

Test the equality of shape parameters of inverse gaussian distributions.

Usage

inverse_gaussian_shape_one_way(x, fctr, conf.level = 0.95)

Arguments

Details

• Null: Null: All shapes are equal. (shape_1 = shape_2 ... shape_k).

• Alternative: At least one shape is not equal.

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)
library(statmod)

# Null is true
set.seed(1)
x <- rinvgauss(n = 150, mean = 1, shape = 2)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
inverse_gaussian_shape_one_way(x, fctr, .95)

# Null is false
set.seed(1)
x <- c(
  rinvgauss(n = 50, mean = 1, shape = 1),
  rinvgauss(n = 50, mean = 1, shape = 3),
  rinvgauss(n = 50, mean = 1, shape = 4)
)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
inverse_gaussian_shape_one_way(x, fctr, .95)

Test the mean of a log normal distribution.

Description

Test the mean of a log normal distribution.

Usage

log_normal_mu_one_sample(x, mu, alternative = "two.sided", conf.level = 0.95)

Arguments

Value

An S3 class containing the test statistic, p value, likelihood based confidence interval, and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rlnorm(100, 0, 1)
log_normal_mu_one_sample(x, 0, "two.sided")

# Null is false
set.seed(1)
x <- rlnorm(100, 3, 1)
log_normal_mu_one_sample(x, 0, "greater")

Test the equality of means of log normal distributions.

Description

Test the equality of means of log normal distributions.

Usage

log_normal_mu_one_way(x, fctr, conf.level = 0.95)

Arguments

Details

• Null: All mus are equal. (mu1 = mu2 ... muk).

• Alternative: At least one mu is not equal.

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rlnorm(150, 1, 1)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
log_normal_mu_one_way(x, fctr, .95)

# Null is false
set.seed(1)
x <- c(rlnorm(50, 1, 1), rlnorm(50, 2, 1), rlnorm(50, 3, 1))
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
log_normal_mu_one_way(x, fctr, .95)

Test the variance of a log normal distribution.

Description

Test the variance of a log normal distribution.

Usage

log_normal_variance_one_sample(
  x,
  sigma.squared,
  alternative = "two.sided",
  conf.level = 0.95
)

Arguments

Value

An S3 class containing the test statistic, p value, likelihood based confidence interval, and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rlnorm(100, 0, 1)
log_normal_variance_one_sample(x, 1, "two.sided")

# Null is false
set.seed(1)
x <- rlnorm(100, 0, 2)
log_normal_variance_one_sample(x, 1, "greater")

Test the equality of variance parameters of log normal distributions.

Description

Test the equality of variance parameters of log normal distributions.

Usage

log_normal_variance_one_way(x, fctr, conf.level = 0.95)

Arguments

Details

• Null: All variances are equal. (o^2_1 = o^2_2 ... o^2_k).

• Alternative: At least one variance is not equal.

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rlnorm(150, 1, 1)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
log_normal_variance_one_way(x, fctr, .95)

# Null is false
set.seed(1)
x <- c(rlnorm(50, 1, 1), rlnorm(50, 1, 2), rlnorm(50, 1, 3))
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
log_normal_variance_one_way(x, fctr, .95)

Test the p parameter of a negative binomial distribution.

Description

Test the p parameter of a negative binomial distribution.

Usage

negative_binomial_p_one_sample(
  num_failures,
  num_successes,
  p,
  alternative = "two.sided",
  conf.level = 0.95
)

Arguments

Value

An S3 class containing the test statistic, p value, likelihood based confidence interval, and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true. 48 failures before 52 successes.
negative_binomial_p_one_sample(48, 52, .50, "two.sided")

# Null is false. 25 failures before 75 successes.
negative_binomial_p_one_sample(25, 75, .50, "two.sided")

Test the equality of p parameters of negative binomial distributions.

Description

Test the equality of p parameters of negative binomial distributions.

Usage

negative_binomial_p_one_way(
  num_failures,
  num_successes,
  fctr,
  conf.level = 0.95
)

Arguments

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true.
set.seed(1)
num_failures <- rnbinom(3, 50, .5)
num_successes <- rep(50, length(num_failures))
fctr <- factor(1:length(num_failures))
negative_binomial_p_one_way(num_failures, num_successes, fctr, .95)


# Null is false
set.seed(1)
num_failures <- rnbinom(3, 50, c(.25, .50, .75))
num_successes <- rep(50, length(num_failures))
fctr <- factor(1:length(num_failures))
negative_binomial_p_one_way(num_failures, num_successes, fctr, .95)

Test the lambda parameter of a poisson distribution.

Description

Test the lambda parameter of a poisson distribution.

Usage

poisson_lambda_one_sample(
  x,
  lambda,
  alternative = "two.sided",
  conf.level = 0.95
)

Arguments

Value

An S3 class containing the test statistic, p value, likelihood based confidence interval, and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rpois(100, 1)
poisson_lambda_one_sample(x, 1, "two.sided")

# Null is false
set.seed(1)
x <- rpois(100, 2)
poisson_lambda_one_sample(x, 1, "greater")

Test the equality of lambda parameters of poisson distributions.

Description

Test the equality of lambda parameters of poisson distributions.

Usage

poisson_lambda_one_way(x, fctr, conf.level = 0.95)

Arguments

Details

• All lambdas are equal. (lambda_1 = lambda_2 ... lambda_k).

• Alternative: At least one lambda is not equal.

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rpois(150, 1)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
poisson_lambda_one_way(x, fctr, .95)

# Null is false
set.seed(1)
x <- c(rpois(50, 1), rpois(50, 2), rpois(50, 3))
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
poisson_lambda_one_way(x, fctr, .95)

Print results of tests.

Description

Print results of tests.

Usage

## S3 method for class 'lrtest'
print(x, ...)

Arguments

Examples

library(LRTesteR)

set.seed(1)
x <- rnorm(100, 0, 1)
test <- gaussian_mu_one_sample(x, 0, "two.sided")
print(test)

set.seed(1)
x <- rnorm(150, 1, 1)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
test <- gaussian_mu_one_way(x, fctr, .95)
print(test)