Package 'likelihoodExplore'

Beta Log Likelihood Function

Description

The log likelihood of a beta density with data, x, shape1, shape2 and ncp parameters.

Usage

likbeta(shape1, shape2, ncp = 0, x, log = FALSE)

Arguments

shape1	non-negative parameters of the Beta distribution.
shape2	non-negative parameters of the Beta distribution.
ncp	non-centrality parameter.
x	vector of quantiles.
log	logical; if TRUE, probabilities p are given as log(p).

Details

The log likelihood is the log of a function of parameters given the data.

Value

A numeric scalar for the log likelihood of the beta density given the data where shape1, shape2, and ncp can be held constant or if vector were given vector will be returned.

Examples

likbeta(x = rbeta(n = 2, shape1 = 3, shape2 = 4),
        shape1 = 3, shape2 = 4)

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Binomial Log Likelihood Function

Description

The log likelihood of a binomial density with data, x, size and prob parameters.

Usage

likbinom(size, prob, x, log = FALSE)

Arguments

size	number of trials (zero or more).
prob	probability of success on each trial.
x	vector of quantiles.
log	logical; if TRUE, probabilities p are given as log(p).

Details

The log likelihood is the log of a function of parameters given the data.

Value

A numeric scalar for the log likelihood of the binomial density given the data where size and prob can be held constant or if vector were given vector will be returned.

Examples

likbinom(x = rbinom(n = 2, size = 3, prob = .4),
        size = 3, prob = .4)

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Cauchy Log Likelihood Function

Description

The log likelihood of a Cauchy density with data, x, location and scale parameters.

Usage

likcauchy(location = 0, scale = 1, x, log = FALSE)

Arguments

location	location and scale parameters.
scale	location and scale parameters.
x	vector of quantiles.
log	logical; if TRUE, probabilities p are given as log(p).

Details

The log likelihood is the log of a function of parameters given the data.

Value

A numeric scalar for the log likelihood of the Cauchy density given the data where location and scale can be held constant or if vector were given vector will be returned.

Examples

likcauchy(x = rcauchy(n = 2))

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Chi-Squared Log Likelihood Function

Description

The log likelihood of a chi-squared density with data, x, df and ncp parameters.

Usage

likchisq(df, ncp = 0, x, log = FALSE)

Arguments

df	degrees of freedom (non-negative, but can be non-integer).
ncp	non-centrality parameter (non-negative).
x	vector of quantiles.
log	logical; if TRUE, probabilities p are given as log(p).

Details

The log likelihood is the log of a function of parameters given the data.

Value

A numeric scalar for the log likelihood of the chi-squared density given the data where df and ncp can be held constant or if vector were given vector will be returned.

Examples

likchisq(x = rchisq(n = 2, df = 4),
        df = 4)

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Likelihood Function Maker

Description

Function that creates a log likelihood function given a density function density.

Usage

likelihood(density, ...)

Arguments

density	density function used
...	other options

Details

The log likelihood is the log of a function of parameters given the data.

Value

A function that is the log likelihood function from density function density.

Examples

likelihood(dnorm, x = rnorm(100))

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Likelihood Exploration

Description

A package of likelihood functions as defined by Fisher <doi:10.1098/rsta.1922.0009> and a function that creates likelihood functions from density functions. The functions are meant to aid in education of likelihood based methods.

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Exponential Log Likelihood Function

Description

The log likelihood of a exponential density with data, x, rate parameter.

Usage

likexp(rate = 1, x, log = FALSE)

Arguments

rate	vector of rates.
x	vector of quantiles.
log	logical; if TRUE, probabilities p are given as log(p).

Details

The log likelihood is the log of a function of parameters given the data.

Value

A numeric scalar for the log likelihood of the exponential density given the data where rate can be held constant or if vector were given vector will be returned.

Examples

likexp(x = rexp(n = 2))

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F Log Likelihood Function

Description

The log likelihood of a F density with data, x, df1, df2 and ncp parameters.

Usage

likf(df1, df2, ncp, x, log = FALSE)

Arguments

df1	degrees of freedom. Inf is allowed.
df2	degrees of freedom. Inf is allowed.
ncp	non-centrality parameter. If omitted the central F is assumed.
x	vector of quantiles.
log	logical; if TRUE, probabilities p are given as log(p).

Details

The log likelihood is the log of a function of parameters given the data.

Value

A numeric scalar for the log likelihood of the f density given the data where df1, df2, and ncp can be held constant or if vector were given vector will be returned.

Examples

likf(x = rf(n = 2, df1 = 3, df2 = 4),
        df1 = 3, df2 = 4, ncp = 0)

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Gamma Log Likelihood Function

Description

The log likelihood of a gamma density with data, x, shape, rate and scale parameters.

Usage

likgamma(shape, rate = 1, scale = 1/rate, x, log = FALSE)

Arguments

shape	shape and scale parameters. Must be positive, scale strictly.
rate	an alternative way to specify the scale.
scale	shape and scale parameters. Must be positive, scale strictly.
x	vector of quantiles.
log	logical; if TRUE, probabilities/densities $p$ are returned as $log(p)$.

Details

The log likelihood is the log of a function of parameters given the data.

Value

A numeric scalar for the log likelihood of the gamma density given the data where shape, scale, and rate can be held constant or if vector were given vector will be returned.

Examples

likgamma(x = rgamma(n = 2, shape = 3),
        shape = 3)

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Geometric Log Likelihood Function

Description

The log likelihood of a geometric density with data, x, prob parameter.

Usage

likgeom(prob, x, log = FALSE)

Arguments

prob	probability of success in each trial. 0 < prob <= 1.
x	vector of quantiles representing the number of failures in a sequence of Bernoulli trials before success occurs.
log	logical; if TRUE, probabilities p are given as log(p).

Details

The log likelihood is the log of a function of parameters given the data.

Value

A numeric scalar for the log likelihood of the geometric density given the data where prob can be held constant or if vector were given vector will be returned.

Examples

likgeom(x = rgeom(n = 2, prob = .4),
        prob = .4)

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Hypergeometric Log Likelihood Function

Description

The log likelihood of a hypergeometric density with data, x, m, n and k parameters.

Usage

likhyper(m, n, k, x, log = FALSE)

Arguments

m	the number of white balls in the urn.
n	the number of black balls in the urn.
k	the number of balls drawn from the urn.
x	vector of quantiles representing the number of white balls drawn without replacement from an urn which contains both black and white balls.
log	logical; if TRUE, probabilities p are given as log(p).

Details

The log likelihood is the log of a function of parameters given the data.

Value

A numeric scalar for the log likelihood of the hypergeometric density given the data where m, n, and k can be held constant or if vector were given vector will be returned.

Examples

likhyper(x = rhyper(nn = 2, m = 3, n = 4, k = 2),
        m = 3, n = 4, k = 2)

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Log Normal Log Likelihood Function

Description

The log likelihood of a log normal density with data, x, meanlog and sdlog parameters.

Usage

liklnorm(meanlog = 0, sdlog = 1, x, log = FALSE)

Arguments

meanlog	mean and standard deviation of the distribution on the log scale with default values of 0 and 1 respectively.
sdlog	mean and standard deviation of the distribution on the log scale with default values of 0 and 1 respectively.
x	vector of quantiles.
log	logical; if TRUE, probabilities p are given as log(p).

Details

The log likelihood is the log of a function of parameters given the data.

Value

A numeric scalar for the log likelihood of the log normal density given the data where meanlog and sdlog can be held constant or if vector were given vector will be returned.

Examples

liklnorm(x = rlnorm(n = 2))

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Logistic Log Likelihood Function

Description

The log likelihood of a logistic density with data, x, location and scale parameters.

Usage

liklogis(location = 0, scale = 1, x, log = FALSE)

Arguments

location	location and scale parameters.
scale	location and scale parameters.
x	vector of quantiles.
log	logical; if TRUE, probabilities p are given as log(p).

Details

The log likelihood is the log of a function of parameters given the data.

Value

A numeric scalar for the log likelihood of the logistic density given the data where location and scale can be held constant or if vector were given vector will be returned.

Examples

liklogis(x = rlogis(n = 2))

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Multinomial Log Likelihood Function

Description

The log likelihood of a multinomial density with data, x, size and prob parameters.

Usage

likmultinom(size = NULL, prob, x, log = FALSE)

Arguments

size	integer, say $N$, specifying the total number of objects that are put into $K$ boxes in the typical multinomial experiment. For dmultinom, it defaults to sum(x).
prob	numeric non-negative vector of length $K$, specifying the probability for the $K$ classes; is internally normalized to sum 1. Infinite and missing values are not allowed.
x	vector of length $K$ of integers in 0:size.
log	logical; if TRUE, log probabilities are computed.

Details

The log likelihood is the log of a function of parameters given the data.

Value

A numeric scalar for the log likelihood of the multinomial density given the data where size and prob can be held constant or if vector were given vector will be returned.

Examples

likmultinom(x = rmultinom(n = 2, size = 3, prob = .4),
        size = 3, prob = .4)

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Negative Binomial Log Likelihood Function

Description

The log likelihood of a negative binomial density with data, x, size, prob and mu parameters.

Usage

liknbinom(size, prob, mu, x, log = FALSE)

Arguments

size	target for number of successful trials, or dispersion parameter (the shape parameter of the gamma mixing distribution). Must be strictly positive, need not be integer.
prob	probability of success in each trial. 0 < prob <= 1.
mu	alternative parametrization via mean: see ‘Details’.
x	vector of (non-negative integer) quantiles.
log	logical; if TRUE, probabilities p are given as log(p).

Details

The log likelihood is the log of a function of parameters given the data.

Value

A numeric scalar for the log likelihood of the negative binomial density given the data where size, prob, and mu can be held constant or if vector were given vector will be returned.

Examples

liknbinom(x = rnbinom(n = 2, size = 3, prob = .4),
        size = 3, prob = .4, mu = NULL)

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Normal Log Likelihood Function

Description

The log likelihood of a normal density with data, x, mean and sd parameters.

Usage

liknorm(mean = 0, sd = 1, x, log = FALSE)

Arguments

mean	vector of means.
sd	vector of standard deviations.
x	vector of quantiles.
log	logical; if TRUE, probabilities p are given as log(p).

Details

The log likelihood is the log of a function of parameters given the data.

Value

A numeric scalar for the log likelihood of the normal density given the data where mean and sd can be held constant or if vector were given vector will be returned.

Examples

liknorm(x = rnorm(n = 2))

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Poisson Log Likelihood Function

Description

The log likelihood of a Poisson density with data, x, lambda parameter.

Usage

likpois(lambda, x, log = FALSE)

Arguments

lambda	vector of (non-negative) means.
x	vector of (non-negative integer) quantiles.
log	logical; if TRUE, probabilities p are given as log(p).

Details

The log likelihood is the log of a function of parameters given the data.

Value

A numeric scalar for the log likelihood of the Poisson density given the data where lambda can be held constant or if vector were given vector will be returned.

Examples

likpois(x = rpois(n = 2, lambda = 4),
        lambda = 4)

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Student's t Log Likelihood Function

Description

The log likelihood of a Student's t density with data, x, df and ncp parameters.

Usage

likt(df, ncp, x, log = FALSE)

Arguments

df	degrees of freedom ($> 0$, maybe non-integer). df = Inf is allowed.
ncp	non-centrality parameter $\delta$; currently except for rt(), only for abs(ncp) <= 37.62. If omitted, use the central t distribution.
x	vector of quantiles.
log	logical; if TRUE, probabilities p are given as log(p).

Details

The log likelihood is the log of a function of parameters given the data.

Value

A numeric scalar for the log likelihood of the Student's t density given the data where df and ncp can be held constant or if vector were given vector will be returned.

Examples

likt(x = rt(n = 2, df = 4),
        df = 4)

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Uniform Log Likelihood Function

Description

The log likelihood of a uniform density with data, x, min and max parameters.

Usage

likunif(min = 0, max = 1, x, log = FALSE)

Arguments

min	lower and upper limits of the distribution. Must be finite.
max	lower and upper limits of the distribution. Must be finite.
x	vector of quantiles.
log	logical; if TRUE, probabilities p are given as log(p).

Details

The log likelihood is the log of a function of parameters given the data.

Value

A numeric scalar for the log likelihood of the uniform density given the data where min and max can be held constant or if vector were given vector will be returned.

Examples

likunif(x = runif(n = 2))

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Weibull Log Likelihood Function

Description

The log likelihood of a Weibull density with data, x, shape and scale parameters.

Usage

likweibull(shape, scale = 1, x, log = FALSE)

Arguments

shape	shape and scale parameters, the latter defaulting to 1.
scale	shape and scale parameters, the latter defaulting to 1.
x	vector of quantiles.
log	logical; if TRUE, probabilities p are given as log(p).

Details

The log likelihood is the log of a function of parameters given the data.

Value

A numeric scalar for the log likelihood of the Weibull density given the data where shape and scale can be held constant or if vector were given vector will be returned.

Examples

likweibull(x = rweibull(n = 2, shape = 3),
        shape = 3)

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Wilcoxon Rank Sum Log Likelihood Function

Description

The log likelihood of a Wilcoxon rank sum density with data, x, m and n parameters.

Usage

likwilcox(m, n, x, log = FALSE)

Arguments

m	numbers of observations in the first and second sample, respectively. Can be vectors of positive integers.
n	numbers of observations in the first and second sample, respectively. Can be vectors of positive integers.
x	vector of quantiles.
log	logical; if TRUE, probabilities p are given as log(p).

Details

The log likelihood is the log of a function of parameters given the data.

Value

A numeric scalar for the log likelihood of the Wilcoxon rank sum density given the data where m and n can be held constant or if vector were given vector will be returned.

Examples

likwilcox(x = rwilcox(nn = 2, m = 3, n = 4),
        m = 3, n = 4)

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