Title:	Estimation of a Lognormal - Generalized Pareto Mixture
Version:	0.1.0
Description:	Estimation of a lognormal - Generalized Pareto mixture via the Expectation-Maximization algorithm. Computation of bootstrap standard errors is supported and performed via parallel computing. Functions for random number simulation and density evaluation are also available. For more details see Bee and Santi (2025) <doi:10.48550/arXiv.2505.22507>.
License:	MIT + file LICENSE
Encoding:	UTF-8
RoxygenNote:	7.3.2
Depends:	R (≥ 4.0.0)
RdMacros:	Rdpack
Imports:	evd, Rdpack, parallel, LNPar, EnvStats
URL:	https://github.com/marco-bee/lognGPD
BugReports:	https://github.com/marco-bee/lognGPD/issues
NeedsCompilation:	no
Packaged:	2025-05-29 08:05:33 UTC; marco.bee
Author:	Marco Bee [aut, cre]
Maintainer:	Marco Bee <marco.bee@unitn.it>
Repository:	CRAN
Date/Publication:	2025-06-02 08:50:05 UTC

Bootstrap standard errors for the MLEs of a lognormal-GPD mixture

Description

This function draws a bootstrap sample and uses it to estimate the parameters of a lognormal-Pareto mixture distribution. Since this is typically called by LPfitEM, see the help of LPfitEM for examples.

Usage

EMBoot(x, x0, y, maxiter)

Arguments

Details

At each bootstrap replication, the mixture is estimated via the EM algorithm.

Value

Estimated parameters obtained from a bootstrap sample.

Mixture estimation via EM

Description

This function estimates a static lognormal - generalized Pareto mixture by means of the EM algorithm. Optionally, bootstrap standard errors are computed via parallel computing.

Usage

EMlogngpdmix(x0, y, maxiter, nboot = 0)

Arguments

Value

A list with the following elements is returned: "p" = estimated value of p, "post" = posterior probabilities of all observations, "mu" = estimated value of \mu, "sigma " = estimated value of \sigma, "xi" = estimated value of \xi, "beta" = estimated value of \beta, "loglik" = maximimzed log-likelihood, "nit" = number of iterations, bootEst = matrix of parameter estimates at each bootstrap replications (only if nboot > 0). bootStd = bootstrap standard errors of each parameter (only if nboot > 0).

Examples

y <- rlognGPD(100,.9,0,1,0.5,2)
x0 <- c(.7,.2,1.3,.8,1.7)
res <- EMlogngpdmix(x0, y, 1000)

Density of the lognormal-GPD mixture

Description

This function evaluates the lognormal-GPD mixture density function.

Usage

dlognGPD(x, p, mu, sigma, xi, beta)

Arguments

Value

ydens (n x 1) vector: numerical values of the lognormal - generalized Pareto mixture at x.

Examples

ydens <- dlognGPD(seq(0,20,length.out=500),.9,0,1,0.5,2)

Density of the lognormal-Pareto spliced distribution

Description

This function evaluates the density of the continuous and differentiable version of the truncated lognormal-Pareto spliced distribution proposed by Scollnik (2007).

Usage

dlognPareto(x, sigma, xmin, alpha)

Arguments

Details

To get a continuous and differentiable density, it is necessary to enforce constraints that reduce the number of free parameters of the model; in particular, the mixing weight and the log-mean of the lognormal distirbution are functions of the reamining parameters. See Scollnik (2007) for details.

Value

ysim (n x 1) vector: numerical values of the truncated lognormal-Pareto spliced distribution at x.

References

Scollnik DPM (2007). “On composite lognormal-Pareto models.” Scandinavian Actuarial Journal, 1, 20-33.

Examples

ysim <- dlognPareto(seq(0,20,length.out=500),1,5,2)

Simulation of the lognormal-GPD mixture

Description

This function simulates a lognormal-GPD mixture.

Usage

rlognGPD(n, p, mu, sigma, xi, beta)

Arguments

Value

ysim (n x 1) vector: n random numbers from the lognormal - generalized Pareto mixture.

Examples

ysim <- rlognGPD(100,.9,0,1,0.5,2)

Simulation of the lognormal-Pareto spliced distribution

Description

This function simulates the continuous and differentiable version of the truncated lognormal-Pareto spliced distribution proposed by Scollnik (2007).

Usage

rlognPareto(n, sigma, xmin, alphapar)

Arguments

Details

See Scollnik (2007) for details.

Value

ysim (nreps x 1) vector: nreps random numbers from the truncated lognormal-Pareto spliced distribution.

References

Scollnik DPM (2007). “On composite lognormal-Pareto models.” Scandinavian Actuarial Journal, 1, 20-33.

Examples

ysim <- rlognPareto(100,1,5,2)

Weighted GPD log-likelihood

Description

This function evaluates the zero-mean generalized Pareto log-likelihood function computed with weighted observations.

Usage

weiGpdLik(x, y, post)

Arguments

Value

llik real: numerical value of the log-likelihood function

Examples

y <- rlognGPD(100,.9,0,1,0.5,2)
x0 <- c(.7,.2,1.3,.8,1.7)
res <- EMlogngpdmix(x0, y, 1000)
llik <- weiGpdLik(c(res$beta,res$xi),y,res$post)