Package 'SujathaDist'

Akaike Information Criterion

Description

Akaike Information Criterion

Usage

## S3 method for class 'fitsujatha'
AIC(object, ...)

Arguments

object	An object of class "fitsujatha".
...	Additional arguments passed to or from other methods.

Value

AIC value.

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Bayesian Information Criterion

Description

Returns the Bayesian Information Criterion (BIC).

Usage

## S3 method for class 'fitsujatha'
BIC(object, ...)

Arguments

object	An object of class "fitsujatha".
...	Additional arguments passed to or from other methods.

Value

A numeric value giving the BIC.

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Coefficients of a fitted Sujatha distribution

Description

Coefficients of a fitted Sujatha distribution

Usage

## S3 method for class 'fitsujatha'
coef(object, ...)

Arguments

object	An object of class "fitsujatha".
...	Additional arguments passed to or from other methods.

Value

Estimated parameter(s).

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Confidence Intervals

Description

Computes Wald confidence intervals.

Usage

## S3 method for class 'fitsujatha'
confint(object, parm = NULL, level = 0.95, ...)

Arguments

object	An object of class "fitsujatha".
parm	Ignored.
level	Confidence level.
...	Additional arguments passed to or from other methods.

Value

Confidence interval matrix.

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Deviance

Description

Deviance

Usage

## S3 method for class 'fitsujatha'
deviance(object, ...)

Arguments

object	An object of class "fitsujatha".
...	Additional arguments passed to or from other methods.

Value

Model deviance.

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Density Function of the Sujatha Distribution

Description

Computes the probability density function (PDF) of the Sujatha distribution.

Usage

dsujatha(x, theta)

Arguments

x	A numeric vector of observations.
theta	A positive parameter.

Value

A numeric vector of density values.

Examples

dsujatha(1, theta = 2)
dsujatha(c(0.5, 1, 2), theta = 3)

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Maximum Likelihood Estimation for the Sujatha Distribution

Description

Fits the Sujatha distribution using Maximum Likelihood Estimation (MLE).

Usage

fitsujatha(x, start = 1, method = "L-BFGS-B")

Arguments

x	A numeric vector of observations.
start	Initial value of theta.
method	Optimization method (default = "L-BFGS-B").

Value

An object of class "fitsujatha" containing

• Estimate

• Standard error

• Variance-covariance matrix

• Hessian matrix

• Log-likelihood

• AIC

• AICc

• BIC

• CAIC

• HQIC

• Deviance

• Convergence status

• Number of iterations

• Original data

Examples

set.seed(123)
x <- rsujatha(100, theta = 2)
fit <- fitsujatha(x)
fit

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Goodness-of-Fit Measures for the Sujatha Distribution

Description

Computes several goodness-of-fit statistics for a fitted Sujatha distribution.

Usage

gofsujatha(object)

Arguments

object

An object of class "fitsujatha".

Value

A list containing

• Log-likelihood

• AIC

• AICc

• BIC

• CAIC

• HQIC

• KS statistic

• KS p-value

• Anderson-Darling statistic

• AD p-value

• Cramer-von Mises statistic

• CVM p-value

• Watson statistic

• Watson p-value

---

Log-likelihood

Description

Log-likelihood

Usage

## S3 method for class 'fitsujatha'
logLik(object, ...)

Arguments

object	An object of class "fitsujatha".
...	Additional arguments passed to or from other methods.

Value

Object of class "logLik".

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Diagnostic Plots for Sujatha Distribution

Description

Produces diagnostic plots for an object of class "fitsujatha".

Usage

## S3 method for class 'fitsujatha'
plot(x, which = 1, ...)

Arguments

x	An object of class "fitsujatha".
which	Integer specifying the plot to draw.
...	Additional arguments passed to or from other methods.

Value

A diagnostic plot.

---

Print a fitted Sujatha distribution

Description

Print a fitted Sujatha distribution

Usage

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

Arguments

x	An object of class "fitsujatha".
...	Additional arguments passed to or from other methods.

Value

Prints the fitted model summary.

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Cumulative Distribution Function of the Sujatha Distribution

Description

Computes the cumulative distribution function (CDF).

Usage

psujatha(q, theta)

Arguments

q	Numeric vector of quantiles.
theta	Positive parameter.

Value

A numeric vector of cumulative probabilities.

Examples

psujatha(1, theta = 2)

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Quantile Function of the Sujatha Distribution

Description

Computes quantiles of the Sujatha distribution by numerically inverting the cumulative distribution function.

Usage

qsujatha(p, theta, lower.tail = TRUE, log.p = FALSE)

Arguments

p	Numeric vector of probabilities.
theta	Positive parameter.
lower.tail	Logical; if TRUE (default), probabilities are P(X <= x).
log.p	Logical; if TRUE, probabilities are given as log(p).

Value

A numeric vector of quantiles.

Examples

qsujatha(0.5, theta = 2)

---

Random Generation from the Sujatha Distribution

Description

Generates random observations from the Sujatha distribution using one of three methods:

• "mixture"Exact Gamma-mixture method (default).

• "inverse"Inverse transform method.

• "rejection"Acceptance-rejection method using an exponential proposal.

Usage

rsujatha(
  n,
  theta,
  method = c("mixture", "inverse", "rejection"),
  lambda = NULL,
  M = NULL
)

Arguments

n	Number of observations.
theta	Positive parameter of the Sujatha distribution.
method	Generation method. One of "mixture", "inverse", or "rejection".
lambda	Rate parameter of the exponential proposal. Used only for the rejection method.
M	Rejection constant. If NULL, it is computed automatically.

Value

A numeric vector of random observations.

Examples

set.seed(123)

## Gamma-mixture method (default)
x1 <- rsujatha(10, theta = 2)

## Inverse transform
x2 <- rsujatha(10, theta = 2, method = "inverse")

## Acceptance-Rejection
x3 <- rsujatha(10,
               theta = 2,
               method = "rejection",
               lambda = 1)

---

Variance-Covariance Matrix

Description

Variance-Covariance Matrix

Usage

## S3 method for class 'fitsujatha'
vcov(object, ...)

Arguments

object	An object of class "fitsujatha".
...	Additional arguments passed to or from other methods.

Value

Variance-covariance matrix.

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