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Utility Functions

Helper functions for parameter initialization

gkwgetstartvalues()
Estimate Distribution Parameters Using Method of Moments

Generalized Kumaraswamy (GKw) - Distribution

Density, CDF, quantile, and random generation (α, β, γ, δ, λ)

dgkw()
Density of the Generalized Kumaraswamy Distribution
pgkw()
Generalized Kumaraswamy Distribution CDF
qgkw()
Generalized Kumaraswamy Distribution Quantile Function
rgkw()
Generalized Kumaraswamy Distribution Random Generation

Generalized Kumaraswamy (GKw) - Inference

Log-likelihood, gradient, and Hessian

llgkw()
Negative Log-Likelihood for the Generalized Kumaraswamy Distribution
grgkw()
Gradient of the Negative Log-Likelihood for the GKw Distribution
hsgkw()
Hessian Matrix of the Negative Log-Likelihood for the GKw Distribution

Beta-Kumaraswamy (BKw) - Distribution

Density, CDF, quantile, and random generation (α, β, γ, δ)

dbkw()
Density of the Beta-Kumaraswamy (BKw) Distribution
pbkw()
Cumulative Distribution Function (CDF) of the Beta-Kumaraswamy (BKw) Distribution
qbkw()
Quantile Function of the Beta-Kumaraswamy (BKw) Distribution
rbkw()
Random Number Generation for the Beta-Kumaraswamy (BKw) Distribution

Beta-Kumaraswamy (BKw) - Inference

Log-likelihood, gradient, and Hessian

llbkw()
Negative Log-Likelihood for Beta-Kumaraswamy (BKw) Distribution
grbkw()
Gradient of the Negative Log-Likelihood for the BKw Distribution
hsbkw()
Hessian Matrix of the Negative Log-Likelihood for the BKw Distribution

Kumaraswamy-Kumaraswamy (KKw) - Distribution

Density, CDF, quantile, and random generation (α, β, δ, λ)

dkkw()
Density of the Kumaraswamy-Kumaraswamy (kkw) Distribution
pkkw()
Cumulative Distribution Function (CDF) of the kkw Distribution
qkkw()
Quantile Function of the Kumaraswamy-Kumaraswamy (kkw) Distribution
rkkw()
Random Number Generation for the kkw Distribution

Kumaraswamy-Kumaraswamy (KKw) - Inference

Log-likelihood, gradient, and Hessian

llkkw()
Negative Log-Likelihood for the kkw Distribution
grkkw()
Gradient of the Negative Log-Likelihood for the kkw Distribution
hskkw()
Hessian Matrix of the Negative Log-Likelihood for the kkw Distribution

Exponentiated Kumaraswamy (EKw) - Distribution

Density, CDF, quantile, and random generation (α, β, λ)

dekw()
Density of the Exponentiated Kumaraswamy (EKw) Distribution
pekw()
Cumulative Distribution Function (CDF) of the EKw Distribution
qekw()
Quantile Function of the Exponentiated Kumaraswamy (EKw) Distribution
rekw()
Random Number Generation for the Exponentiated Kumaraswamy (EKw) Distribution

Exponentiated Kumaraswamy (EKw) - Inference

Log-likelihood, gradient, and Hessian

llekw()
Negative Log-Likelihood for the Exponentiated Kumaraswamy (EKw) Distribution
grekw()
Gradient of the Negative Log-Likelihood for the EKw Distribution
hsekw()
Hessian Matrix of the Negative Log-Likelihood for the EKw Distribution

McDonald (MC) - Distribution

Density, CDF, quantile, and random generation (γ, δ, λ)

dmc()
Density of the McDonald (Mc)/Beta Power Distribution Distribution
pmc()
CDF of the McDonald (Mc)/Beta Power Distribution
qmc()
Quantile Function of the McDonald (Mc)/Beta Power Distribution
rmc()
Random Number Generation for the McDonald (Mc)/Beta Power Distribution

McDonald (MC) - Inference

Log-likelihood, gradient, and Hessian

llmc()
Negative Log-Likelihood for the McDonald (Mc)/Beta Power Distribution
grmc()
Gradient of the Negative Log-Likelihood for the McDonald (Mc)/Beta Power Distribution
hsmc()
Hessian Matrix of the Negative Log-Likelihood for the McDonald (Mc)/Beta Power Distribution

Kumaraswamy (Kw) - Distribution

Density, CDF, quantile, and random generation (α, β)

dkw()
Density of the Kumaraswamy (Kw) Distribution
pkw()
Cumulative Distribution Function (CDF) of the Kumaraswamy (Kw) Distribution
qkw()
Quantile Function of the Kumaraswamy (Kw) Distribution
rkw()
Random Number Generation for the Kumaraswamy (Kw) Distribution

Kumaraswamy (Kw) - Inference

Log-likelihood, gradient, and Hessian

llkw()
Negative Log-Likelihood of the Kumaraswamy (Kw) Distribution
grkw()
Gradient of the Negative Log-Likelihood for the Kumaraswamy (Kw) Distribution
hskw()
Hessian Matrix of the Negative Log-Likelihood for the Kw Distribution

Beta - Distribution

Density, CDF, quantile, and random generation (γ, δ)

dbeta_()
Density of the Beta Distribution (gamma, delta+1 Parameterization)
pbeta_()
CDF of the Beta Distribution (gamma, delta+1 Parameterization)
qbeta_()
Quantile Function of the Beta Distribution (gamma, delta+1 Parameterization)
rbeta_()
Random Generation for the Beta Distribution (gamma, delta+1 Parameterization)

Beta - Inference

Log-likelihood, gradient, and Hessian

llbeta()
Negative Log-Likelihood for the Beta Distribution (gamma, delta+1 Parameterization)
grbeta()
Gradient of the Negative Log-Likelihood for the Beta Distribution (gamma, delta+1 Parameterization)
hsbeta()
Hessian Matrix of the Negative Log-Likelihood for the Beta Distribution (gamma, delta+1 Parameterization)