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matrixdist

Statistics for Matrix Distributions

This package implements tools which are useful for the statistical analysis of discrete, continuous, multivariate, right-censored or regression variants of phase-type distributions. These distributions are absorption times of Markov jump processes, and thus the maximization of their likelihood for statistical estimation is best dealt with using the EM algorithm.

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install.packages('matrixdist')

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Version

1.1.9

License

GPL-3

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Repository

https://github.com/martinbladt/matrixdist_1.0

Maintainer

Martin Bladt

Last Published

August 8th, 2023

Functions in matrixdist (1.1.9)

EM step for the mPH class with right-censoring, for different marginal sub-intensity matrices

LRT,ph,ph-method

LRT method for ph class

Fisher,sph-method

Fisher information method for sph class

EM for discrete phase-type

New generic for obtaining the Fisher information of survival matrix distributions

TVR Method for dph Class

New generic for likelihood ratio test between two matrix distribution models

EM for discrete phase-type MoE

Nfold,dph-method

Nfold method for phase-type distributions

TVR method for ph class

MoE method for ph Class

EM for phase-type distributions using Pade approximation for matrix exponential

Bivariate discrete phase-type distributions

EM step for phase-type using Runge-Kutta

New generic for mixture-of-experts regression with matrix distributions

Constructor function for bivariate discrete phase-type distributions

New generic for transformation via rewards of a matrix distribution

New generic for N-fold convolution of two matrix distributions

New generic for the distribution of matrix distributions

MPHstar_EMstep_UNI

EM step using Uniformization for MPHstar class

EM for phase-type using uniformization for matrix exponential

Bivariate discrete phase-type joint density of the feed forward type

Runge-Kutta for the calculation of the a vector in a EM step

Bivariate discrete phase-type joint tail of the feed forward type

Distribution method for inhomogeneous phase-type distributions

EM for discrete bivariate phase-type

MPHstar_data_aggregation

Prepare data for the MPHstar_EMstep_UNI

Bivariate phase-type joint tail of the feed forward type

Multivariate phase-type distributions obtained by transformation via rewards

cdf,miph-method

Distribution method for multivariate inhomogeneous phase-type distributions

default_step_length

Default size of the steps in the RK

MoE,bivdph-method

MoE method for bivdph Class

MoE method for dph Class

Bivariate inhomogeneous phase-type distributions

EMstep_bivdph_MoE

EM for discrete bivariate phase-type MoE

Constructor function for bivariate inhomogeneous phase-type distributions

dens,bivdph-method

Density method for bivariate discrete phase-type distributions

EM for bivariate phase-type distributions using Pade for matrix exponential

Distribution method for multivariate phase-type distributions

dens,mdph-method

Density method for multivariate discrete phase-type distributions

dens,miph-method

Density method for multivariate inhomogeneous phase-type distributions

coef,mdph-method

Coef method for mdph class

Distribution method for phase-type distributions

EM for multivariate discrete phase-type

Constructor function for multivariate phase-type distributions (MPH* class)

EMstep_mdph_MoE

EM for multivariate discrete phase-type MoE

coef,dph-method

Coef method for dph Class

MoE,mdph-method

MoE method for mdph Class

fit,bivdph-method

Fit method for bivdph Class

Coef method for ph class

coef,iph-method

Coef method for iph class

cor,bivdph-method

Cor method for bivdph class

coef,bivdph-method

Coef method for bivdph class

dens,biviph-method

Density method for bivariate inhomogeneous phase-type distributions

fit,bivph-method

Fit method for bivph Class

cor,mdph-method

Cor method for multivariate discrete phase-type distributions

Distribution method for discrete phase-type distributions

cor,bivph-method

Cor method for bivph class

Fit method for mph/miph class, using mixture-of-experts regression

linCom,bivph-method

Linear combination method for bivariate phase-type distributions

Cor method for multivariate phase-type distributions

Discrete phase-type cdf

New generic for linear combinations of multivariate matrix distributions

logLikelihoodMgompertz_RK

Loglikelihood of matrix-Gompertz using Runge-Kutta

logLikelihoodMloglogistic_RK

Loglikelihood of matrix-loglogistic using Runge-Kutta

coef,biviph-method

Coef method for biviph class

New generic for the density of matrix distributions

dens,bivph-method

Density method for bivariate phase-type distributions

Discrete phase-type distributions

coef,bivph-method

Coef method for bivph class

logLikelihoodMgompertz_UNIs

Loglikelihood of PI with matrix-Gompertz using Uniformization

Constructor function for discrete phase-type distributions

Discrete phase-type density

Bivariate phase-type distributions

dens,dph-method

Density method for discrete phase-type distributions

dens,iph-method

Density method for inhomogeneous phase-type distributions

New generic for evaluating survival matrix distributions

expm terms of phase-type likelihood using uniformization

logLikelihoodMloglogistic_PADE

Loglikelihood of matrix-loglogistic using Pade

Constructor function for bivariate phase-type distributions

logLikelihoodMlognormal_PADE

Loglikelihood of matrix-lognormal using Pade

Bivariate phase-type joint density of the feed forward type

Pgf of a discrete phase-type distribution

Bivariate phase-type joint Laplace

logLikelihoodMlognormal_PADEs

Loglikelihood of PI with matrix-lognormal using Pade

logLikelihoodMpareto_UNI

Loglikelihood of matrix-Pareto using uniformization

Matrix exponential

Find weight of observations

fit,MPHstar-method

Fit method for mph class

Find n such that P(N > n) = h with N Poisson distributed

coef,sph-method

Coef method for sph Class

logLikelihoodMpareto_UNIs

Loglikelihood of PI with matrix-Pareto using uniformization

Fit method for dph class

cor,MPHstar-method

Cor method for MPHstar class

Fit method for mph Class

fit,mdph-method

Fit method for mdph Class

Fit method for ph class

logLikelihoodMlognormal_RK

Loglikelihood of matrix-lognormal using Runge-Kutta

New generic for estimating matrix distributions

logLikelihoodMpareto_RK

Loglikelihood of matrix-Pareto using Runge-Kutta

New generic for the hazard rate of matrix distributions

logLikelihoodPH_RK

Loglikelihood of phase-type using Runge-Kutta

laplace,mph-method

Laplace method for multivariate phase-type distributions

laplace,ph-method

Laplace method for phase-type distributions

Hazard rate method for phase-type distributions

logLikelihoodPH_RKs

Loglikelihood of PI with phase-type using Runge-Kutta

cumulate_matrix

Cumulate matrix

mloglogisticcdf

Matrix-loglogistic cdf

Matrix-Gompertz density

logLikelihoodMweibull_RK

Loglikelihood of matrix-Weibull using Runge-Kutta

matrix_exponential

Matrix exponential

logLikelihoodMgev_PADE

Loglikelihood of matrix-GEV using Pade

Inverse of a matrix

logLikelihoodMloglogistic_PADEs

Loglikelihood of PI with matrix-loglogistic using Pade

logLikelihoodMgompertz_PADE

Loglikelihood of matrix-Gompertz using Pade

mean,dph-method

Mean method for discrete phase-type distributions

mean,mdph-method

Mean method for multivariate discrete phase-type distributions

logLikelihoodMgompertz_PADEs

Loglikelihood of PI with matrix-Gompertz using Pade

Constructor function for phase-type distributions

cumulate_vector

Cumulate vector

dens,mph-method

Density method for multivariate phase-type distributions

logLikelihoodMloglogistic_UNI

Loglikelihood of matrix-loglogistic using uniformization

Density method for phase-type distributions

New generic for Laplace transform of matrix distributions

L inf norm of a matrix

New generic for mgf of matrix distributions

logLikelihoodMloglogistic_UNIs

Loglikelihood of PI with matrix-loglogistic using uniformization

Constructor function for inhomogeneous phase-type distributions

linCom,MPHstar-method

Linear combination method for MPHstar class

Embedded Markov chain of a sub-intensity matrix

logLikelihoodMloglogistic_RKs

Loglikelihood of PI with matrix-loglogistic using Runge-Kutta

linear_combination

Computes PH parameters of a linear combination of vector from MPHstar

evaluate,sph-method

Evaluation method for sph Class

Initial state of Markov jump process

logLikelihoodMpareto_PADEs

Loglikelihood of PI with matrix-Pareto using Pade

logLikelihoodMpareto_RKs

Loglikelihood of PI with matrix-Pareto using Runge-Kutta

logLik,ph-method

Loglikelihood method for ph class

minimum,dph,dph-method

Minimum method for discrete phase-type distributions

laplace,bivph-method

Laplace method for bivph class

logLikelihoodMgev_RK

Loglikelihood of matrix-GEV using Runge-Kutta

logLikelihoodMweibull_PADE

Loglikelihood of matrix-Weibull using Pade

logLikelihoodMgompertz_RKs

Loglikelihood of PI with matrix-Gompertz using Runge-Kutta

logLikelihoodMweibull_PADEs

Loglikelihood of PI with matrix-Weibull using Pade

logLikelihoodbivPH

Loglikelihood for Bivariate PH

logLikelihoodMgompertz_UNI

Loglikelihood of matrix-Gompertz using uniformization

New state in a Markov jump process

logLikelihoodMgev_UNI

Loglikelihood of matrix-GEV using uniformization

logLikelihoodMweibull_RKs

Loglikelihood of PI with matrix-Weibull using Runge-Kutta

logLikelihoodMweibull_UNI

Loglikelihood of matrix-Weibull using uniformization

logLikelihoodmDPH

Loglikelihood for multivariate discrete phase-type

logLikelihoodPH_UNI

Loglikelihood of phase-type using uniformization

logLikelihoodPH_UNIs

Loglikelihood of PI with phase-type using uniformization

logLikelihoodbivDPH_MoE

Loglikelihood for bivariate discrete phase-type MoE

mixture,ph,ph-method

Mixture method for phase-type distributions

logLikelihoodMlognormal_RKs

Loglikelihood of PI matrix-lognormal using Runge-Kutta

New generic for mixture of two matrix distributions

logLikelihoodbivDPH

Loglikelihood for bivariate discrete phase-type

Matrix-lognormal density

Matrix-Pareto density

Inhomogeneous phase-type distributions

Matrix-Pareto cdf

rew_sanity_check

Transform a reward matrix with very small rewards to avoid numerical problems

logLikelihoodDPH

Loglikelihood for discrete phase-type

logLikelihoodMlognormal_UNI

Loglikelihood of matrix-lognormal using uniformization

pgf,bivdph-method

Pgf method for bivariate discrete phase-type distributions

mloglogisticden

Matrix-loglogistic density

Matrix-lognormal cdf

logLikelihoodPH_PADE

Loglikelihood of phase-type using Pade approximation

sim,biviph-method

Simulation method for bivariate inhomogeneous phase-type distributions

logLikelihoodPH_PADEs

Loglikelihood of PI with phase-type using Pade

logLikelihoodDPH_MoE

Loglikelihood for discrete phase-type MoE

marginal,MPHstar-method

Marginal method for MPHstar class

marginal,bivdph-method

Marginal method for bivdph class

marginal,mph-method

Marginal method for multivariate phase-type distributions

logLikelihoodMlognormal_UNIs

Loglikelihood of PI with matrix-lognormal using uniformization

show,miph-method

Show method for multivariate inhomogeneous phase-type distributions

New generic for the marginals of multivariate matrix distributions

logLikelihoodMpareto_PADE

Loglikelihood of matrix-Pareto using Pade

minimum,iph,iph-method

Minimum method for inhomogeneous phase-type distributions

Computes exp(Sx) via series representation

Product of two matrices

minimum,ph,ph-method

Minimum method for phase-type distributions

mean,bivdph-method

Mean method for bivdph class

logLikelihoodMweibull_UNIs

Loglikelihood of PI with matrix-Weibull using uniformization

Matrix-Weibull cdf

marginal_expectation

Marginal conditional expectations

maximum,iph,iph-method

Maximum method for inhomogeneous phase-type distributions

mean,bivph-method

Mean Method for bivph class

marginal,mdph-method

Marginal method for mdph class

logLikelihoodPH_MoE

Loglikelihood for PH-MoE

Creates the matrix (A1, B1 ; 0, A2)

logLikelihoodmDPH_MoE

Loglikelihood for multivariate discrete phase-type MoE

Constructor function for multivariate phase-type distributions

marginal,miph-method

Marginal method for multivariate inhomogeneous phase-type distributions

Laplace transform of a phase-type distribution

Matrix-GEV density

Performs TVR for phase-type distributions

matrixdist-package

Statistics for Matrix Distributions

Find how many states have positive reward

+,dph,dph-method

Sum method for discrete phase-type distributions

Sum method for phase-type distributions

mgf,bivph-method

Mgf method for bivph class

Regression method for ph Class

Simulate discrete phase-type

mean,MPHstar-method

Mean method for MPHstar class

maximum,dph,dph-method

Maximum method for discrete phase-type distributions

Random inhomogeneous phase-type

revers_data_trans

Applies the inverse of the GEV transformation but giving back the resulting vector in reverse order

New generic for regression with matrix distributions

Constructor function for multivariate discrete phase-type distributions

show,mph-method

Show method for multivariate phase-type distributions

sim,MPHstar-method

Simulation method for multivariate phase-type distributions

Mean method for phase-type distributions

Survival analysis for phase-type distributions

New generic for simulating matrix distributions

Mgf method for phase-type distributions

sim,bivdph-method

Simulation method for bivariate discrete phase-type distributions

Matrix-Gompertz cdf

sim,mdph-method

Simulation method for multivariate discrete phase-type distributions

Maximum diagonal element of a matrix

show,biviph-method

Show method for bivariate inhomogeneous phase-type distributions

Constructor function for multivariate inhomogeneous phase-type distributions

Matrix-Weibull density

Multivariate phase-type distributions

show,iph-method

Show method for inhomogeneous phase-type distributions

sim,miph-method

Simulation method for inhomogeneous multivariate phase-type distributions

var,bivdph-method

Var method for bivdph class

mean,mph-method

Mean method for multivariate phase-type distributions

var,MPHstar-method

Var method for MPHstar class

Multivariate discrete phase-type distributions

Multivariate discrete phase-type density

var,bivph-method

Var method for bivph class

mixture,dph,dph-method

Mixture method for phase-type distributions

marginal,biviph-method

Marginal method for biviph class

New generic for pgf of matrix distributions

vector_of_powers

Computes elements A^n until the given size

Mgf method for multivariate phase-type distributions

moment,mph-method

Moment method for multivariate phase-type distributions

Pgf Method for discrete phase-type distributions

moment,mdph-method

Moment method for multivariate discrete phase-type distributions

moment,ph-method

Moment method for phase-type distributions

moment,bivdph-method

Moment method for bivdph class

moment,bivph-method

Moment method for bivph class

marginal,bivph-method

Marginal method for bivph class

pgf,mdph-method

Pgf method for multivariate discrete phase-type distributions

Computes the initial distribution and sub-intensity of the sum of two discrete phase-type distributed random variables

Phase-type distributions

Merges the matrices S11, S12 and S22 into a sub-intensity matrix

maximum,ph,ph-method

Maximum method for phase-type distributions

Simulate a MPH* random vector

moment,dph-method

Moment method for discrete phase-type distributions

Runge-Kutta for the calculation of the a and b vectors and the c matrix in a EM step

Find which states have positive reward

Simulate a MIPH* random vector

Performs TVR for discrete phase-type distributions

Computes A^(2^n)

Var method for discrete phase-type distributions

sim,bivph-method

Simulation method for bivariate phase-type distributions

random_structure

Random structure of a phase-type

show,MPHstar-method

Show method for multivariate phase-type distributions

Computes the initial distribution and sub-intensity of the sum of two phase-type distributed random variables.

random_structure_bivph

Random structure of a bivariate phase-type

Random reward matrix

New generic for maximum of two matrix distributions

New generic for moments of matrix distributions

vector_of_matrices

Computes the elements S^n / n! until the a given size

Random matrix GEV

show,mdph-method

Show method for multivariate discrete phase-type distributions

Var method for multivariate phase-type distributions

var,mdph-method

Var method for multivariate discrete phase-type distributions

Phase-type density

Simulate phase-type

show,sph-method

Show method for survival phase-type objects

Var method for phase-type distributions

vector_of_matrices_2

Computes the elements S^n / n! until given value of n

Show method for phase-type distributions

Simulation method for multivariate phase-type distributions

Simulation method for phase-type distributions

New generic for minimum of two matrix distributions

Multivariate inhomogeneous phase-type distributions

show,bivdph-method

Show method for bivariate discrete phase-type distributions

Quantile method for phase-type distributions

Simulation method for phase-type distributions

New generic for the quantile of matrix distributions

show,bivph-method

Show method for bivariate phase-type distributions

Constructor function for survival phase-type objects

show,dph-method

Show method for discrete phase-type distributions

Simulation method for inhomogeneous phase-type distributions

EMstep_MoE_PADE