Statistics for Matrix Distributions
New generic for likelihood ratio test between two matrix distribution ...
Matrix-Gompertz cdf
Matrix-Gompertz density
Minimum method for discrete phase-type distributions
LRT method for ph class
Loglikelihood of phase-type using Runge-Kutta
Loglikelihood of PI with phase-type using Runge-Kutta
Loglikelihood of phase-type using uniformization
Loglikelihood of PI with phase-type using uniformization
Computes exp(Sx) via series representation
Marginal method for bivdph class
Marginal method for biviph class
Marginal method for bivph class
Marginal method for mdph class
Marginal method for multivariate inhomogeneous phase-type distribution...
Marginal method for multivariate phase-type distributions
Marginal method for MPHstar class
New generic for the marginals of multivariate matrix distributions
Marginal conditional expectations
Matrix exponential
Inverse of a matrix
Computes A^n
Product of two matrices
Creates the matrix (A1, B1 ; 0, A2)
MoE method for mdph Class
Regression method for ph Class
New generic for regression with matrix distributions
Applies the inverse of the GEV transformation but giving back the resu...
Transform a reward matrix with very small rewards to avoid numerical p...
Random inhomogeneous phase-type
Random matrix GEV
Simulate MDPH*
Simulate a MIPH* random vector
Simulate a MPH* random vector
Simulate phase-type
Runge-Kutta for the calculation of the a and b vectors and the c matri...
Show method for bivariate discrete phase-type distributions
Show method for bivariate inhomogeneous phase-type distributions
Show method for bivariate phase-type distributions
Show method for discrete phase-type distributions
Show method for inhomogeneous phase-type distributions
Show method for multivariate discrete phase-type distributions
Show method for multivariate inhomogeneous phase-type distributions
Show method for multivariate phase-type distributions
Show method for multivariate phase-type distributions
Show method for phase-type distributions
Show method for survival phase-type objects
Simulation method for bivariate discrete phase-type distributions
Simulation method for bivariate inhomogeneous phase-type distributions
Simulation method for bivariate phase-type distributions
Simulation method for phase-type distributions
Simulation method for inhomogeneous phase-type distributions
Simulation method for multivariate discrete phase-type distributions
Simulation method for inhomogeneous multivariate phase-type distributi...
Simulation method for multivariate phase-type distributions
Simulation method for multivariate phase-type distributions
Simulation method for phase-type distributions
New generic for simulating matrix distributions
Survival analysis for phase-type distributions
Constructor function for survival phase-type objects
Computes the initial distribution and sub-intensity of the sum of two ...
Computes the initial distribution and sub-intensity of the sum of two ...
TVR Method for dph Class
TVR method for ph class
New generic for transformation via rewards of a matrix distribution
Performs TVR for discrete phase-type distributions
Performs TVR for phase-type distributions
Var method for bivdph class
Var method for bivph class
Var method for discrete phase-type distributions
Var method for multivariate discrete phase-type distributions
Var method for multivariate phase-type distributions
Var method for MPHstar class
Var method for phase-type distributions
Computes the elements S^n / n! until the a given size
Computes the elements S^n / n! until given value of n
Computes elements A^n until the given size
Statistics for Matrix Distributions
Maximum diagonal element of a matrix
Maximum method for discrete phase-type distributions
Maximum method for inhomogeneous phase-type distributions
Maximum method for phase-type distributions
New generic for maximum of two matrix distributions
Multivariate discrete phase-type distributions
Constructor function for multivariate discrete phase-type distribution...
Multivariate discrete phase-type density
Mean method for bivdph class
Mean Method for bivph class
Mean method for discrete phase-type distributions
Mean method for multivariate discrete phase-type distributions
Mean method for multivariate phase-type distributions
Mean method for MPHstar class
Mean method for phase-type distributions
Merges the matrices S11, S12 and S22 into a sub-intensity matrix
Matrix-GEV cdf
Matrix-GEV density
Mgf method for bivph class
Mgf method for multivariate phase-type distributions
Mgf method for phase-type distributions
New generic for mgf of matrix distributions
Minimum method for inhomogeneous phase-type distributions
Minimum method for phase-type distributions
New generic for minimum of two matrix distributions
Multivariate inhomogeneous phase-type distributions
Constructor function for multivariate inhomogeneous phase-type distrib...
Mixture method for phase-type distributions
Mixture method for phase-type distributions
New generic for mixture of two matrix distributions
Matrix-loglogistic cdf
Matrix-loglogistic density
Matrix-lognormal cdf
Matrix-lognormal density
MoE method for bivdph Class
MoE method for dph Class
Fit method for mph/miph class, using mixture-of-experts regression
MoE method for ph Class
New generic for mixture-of-experts regression with matrix distribution...
Moment method for bivdph class
Moment method for bivph class
Moment method for discrete phase-type distributions
Moment method for multivariate discrete phase-type distributions
Moment method for multivariate phase-type distributions
Moment method for phase-type distributions
New generic for moments of matrix distributions
Matrix-Pareto cdf
Matrix-Pareto density
Multivariate phase-type distributions
Constructor function for multivariate phase-type distributions
Multivariate phase-type distributions obtained by transformation via r...
Constructor function for multivariate phase-type distributions (MPH* c...
Prepare data for the MPHstar_EMstep_UNI
EM step using Uniformization for MPHstar class
Matrix-Weibull cdf
Matrix-Weibull density
Find how many states have positive reward
New state in a Markov jump process
Nfold method for phase-type distributions
New generic for N-fold convolution of two matrix distributions
Pgf method for bivariate discrete phase-type distributions
Pgf Method for discrete phase-type distributions
Pgf method for multivariate discrete phase-type distributions
New generic for pgf of matrix distributions
Phase-type distributions
Constructor function for phase-type distributions
Laplace transform of a phase-type distribution
Phase-type cdf
Phase-type density
Sum method for discrete phase-type distributions
Sum method for phase-type distributions
Find which states have positive reward
Computes A^(2^n)
Quantile method for phase-type distributions
New generic for the quantile of matrix distributions
Random reward matrix
Random structure of a phase-type
Random structure of a bivariate phase-type
Simulate discrete phase-type
Runge-Kutta for the calculation of the a vector in a EM step
Bivariate discrete phase-type distributions
Constructor function for bivariate discrete phase-type distributions
Bivariate discrete phase-type joint density of the feed forward type
Bivariate discrete phase-type joint tail of the feed forward type
Bivariate inhomogeneous phase-type distributions
Constructor function for bivariate inhomogeneous phase-type distributi...
Bivariate phase-type distributions
Constructor function for bivariate phase-type distributions
Bivariate phase-type joint density of the feed forward type
Bivariate phase-type joint Laplace
Bivariate phase-type joint tail of the feed forward type
Distribution method for discrete phase-type distributions
Distribution method for inhomogeneous phase-type distributions
Distribution method for multivariate inhomogeneous phase-type distribu...
Distribution method for multivariate phase-type distributions
Distribution method for phase-type distributions
New generic for the distribution of matrix distributions
Clone a matrix
Clone a vector
Coef method for bivdph class
Coef method for biviph class
Coef method for bivph class
Coef method for dph Class
Coef method for iph class
Coef method for mdph class
Coef method for ph class
Coef method for sph Class
Cor method for bivdph class
Cor method for bivph class
Cor method for multivariate discrete phase-type distributions
Cor method for multivariate phase-type distributions
Cor method for MPHstar class
Cumulate matrix
Cumulate vector
Default size of the steps in the RK
Density method for bivariate discrete phase-type distributions
Density method for bivariate inhomogeneous phase-type distributions
Density method for bivariate phase-type distributions
Density method for discrete phase-type distributions
Density method for inhomogeneous phase-type distributions
Density method for multivariate discrete phase-type distributions
Density method for multivariate inhomogeneous phase-type distributions
Density method for multivariate phase-type distributions
Density method for phase-type distributions
New generic for the density of matrix distributions
Discrete phase-type distributions
Constructor function for discrete phase-type distributions
Pgf of a discrete phase-type distribution
Discrete phase-type cdf
Discrete phase-type density
EM step for the mPH class with right-censoring, for different marginal...
Embedded Markov chain of a sub-intensity matrix
EM for discrete bivariate phase-type
EM for discrete bivariate phase-type MoE
EM for bivariate phase-type distributions using Pade for matrix expone...
EM for discrete phase-type
EM for discrete phase-type MoE
EM for multivariate discrete phase-type
EM for multivariate discrete phase-type MoE
EM for PH-MoE
EM for phase-type distributions using Pade approximation for matrix ex...
EM step for phase-type using Runge-Kutta
EM for phase-type using uniformization for matrix exponential
Evaluation method for sph Class
New generic for evaluating survival matrix distributions
expm terms of phase-type likelihood using uniformization
Matrix exponential
Find n such that P(N > n) = h with N Poisson distributed
Find weight of observations
Fisher information method for sph class
New generic for obtaining the Fisher information of survival matrix di...
Fit method for bivdph Class
Fit method for bivph Class
Fit method for dph class
Fit method for mdph Class
Fit method for mph Class
Fit method for mph class
Fit method for ph class
New generic for estimating matrix distributions
Hazard rate method for phase-type distributions
New generic for the hazard rate of matrix distributions
L inf norm of a matrix
Initial state of Markov jump process
Inhomogeneous phase-type distributions
Constructor function for inhomogeneous phase-type distributions
Laplace method for bivph class
Laplace method for multivariate phase-type distributions
Laplace method for phase-type distributions
New generic for Laplace transform of matrix distributions
Linear combination method for bivariate phase-type distributions
Linear combination method for MPHstar class
New generic for linear combinations of multivariate matrix distributio...
Computes PH parameters of a linear combination of vector from MPHstar
Loglikelihood method for ph class
Loglikelihood for bivariate discrete phase-type
Loglikelihood for bivariate discrete phase-type MoE
Loglikelihood for Bivariate PH
Loglikelihood for discrete phase-type
Loglikelihood for discrete phase-type MoE
Loglikelihood for multivariate discrete phase-type
Loglikelihood for multivariate discrete phase-type MoE
Loglikelihood of matrix-GEV using Pade
Loglikelihood of matrix-GEV using Runge-Kutta
Loglikelihood of matrix-GEV using uniformization
Loglikelihood of matrix-Gompertz using Pade
Loglikelihood of PI with matrix-Gompertz using Pade
Loglikelihood of matrix-Gompertz using Runge-Kutta
Loglikelihood of PI with matrix-Gompertz using Runge-Kutta
Loglikelihood of matrix-Gompertz using uniformization
Loglikelihood of PI with matrix-Gompertz using Uniformization
Loglikelihood of matrix-loglogistic using Pade
Loglikelihood of PI with matrix-loglogistic using Pade
Loglikelihood of matrix-loglogistic using Runge-Kutta
Loglikelihood of PI with matrix-loglogistic using Runge-Kutta
Loglikelihood of matrix-loglogistic using uniformization
Loglikelihood of PI with matrix-loglogistic using uniformization
Loglikelihood of matrix-lognormal using Pade
Loglikelihood of PI with matrix-lognormal using Pade
Loglikelihood of matrix-lognormal using Runge-Kutta
Loglikelihood of PI matrix-lognormal using Runge-Kutta
Loglikelihood of matrix-lognormal using uniformization
Loglikelihood of PI with matrix-lognormal using uniformization
Loglikelihood of matrix-Pareto using Pade
Loglikelihood of PI with matrix-Pareto using Pade
Loglikelihood of matrix-Pareto using Runge-Kutta
Loglikelihood of PI with matrix-Pareto using Runge-Kutta
Loglikelihood of matrix-Pareto using uniformization
Loglikelihood of PI with matrix-Pareto using uniformization
Loglikelihood of matrix-Weibull using Pade
Loglikelihood of PI with matrix-Weibull using Pade
Loglikelihood of matrix-Weibull using Runge-Kutta
Loglikelihood of PI with matrix-Weibull using Runge-Kutta
Loglikelihood of matrix-Weibull using uniformization
Loglikelihood of PI with matrix-Weibull using uniformization
Loglikelihood for PH-MoE
Loglikelihood of phase-type using Pade approximation
Loglikelihood of PI with phase-type using Pade
Tools for phase-type distributions including the following variants: continuous, discrete, multivariate, in-homogeneous, right-censored, and regression. Methods for functional evaluation, simulation and estimation using the expectation-maximization (EM) algorithm are provided for all models. The methods of this package are based on the following references. Asmussen, S., Nerman, O., & Olsson, M. (1996). Fitting phase-type distributions via the EM algorithm, Olsson, M. (1996). Estimation of phase-type distributions from censored data, Albrecher, H., & Bladt, M. (2019) <doi:10.1017/jpr.2019.60>, Albrecher, H., Bladt, M., & Yslas, J. (2022) <doi:10.1111/sjos.12505>, Albrecher, H., Bladt, M., Bladt, M., & Yslas, J. (2022) <doi:10.1016/j.insmatheco.2022.08.001>, Bladt, M., & Yslas, J. (2022) <doi:10.1080/03461238.2022.2097019>, Bladt, M. (2022) <doi:10.1017/asb.2021.40>, Bladt, M. (2023) <doi:10.1080/10920277.2023.2167833>, Albrecher, H., Bladt, M., & Mueller, A. (2023) <doi:10.1515/demo-2022-0153>, Bladt, M. & Yslas, J. (2023) <doi:10.1016/j.insmatheco.2023.02.008>.
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