Package: StochFracPoisson 0.1.0

StochFracPoisson: Stochastic Poisson Processes and Fractional Counting Models

Implementation of advanced stochastic counting processes. Main models include the Fractional Counting Process at Levy times (Garg et al. (2025) <doi:10.1007/s10955-025-03515-9>), the Generalized Iterated Poisson Process (Soni & Pathak (2024) <doi:10.1007/s10959-024-01362-0>), the Generalized Fractional Risk Process (Soni & Pathak (2024) <doi:10.1007/s11009-024-10111-z>), and the Tempered Space-Time Fractional Negative Binomial Process (Garg et al. (2025) <doi:10.1007/s11009-025-10179-1>).

Authors:Shikhar Tyagi [aut, cre], Vrijesh Tripathi [aut]

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manual.pdf |manual.html✨
DESCRIPTION
card.svg |card.png
StochFracPoisson/json (API)

# Install 'StochFracPoisson' in R:
install.packages('StochFracPoisson', repos = c('https://shikhartyagi.r-universe.dev', 'https://cloud.r-project.org'))

On CRAN:

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This package does not link to any Github/Gitlab/R-forge repository. No issue tracker or development information is available.

1.70 score 182 downloads 76 exports 0 dependencies

Last updated from:172d3fc4af. Checks:9 OK. Indexed: yes.

TargetResultTimeFilesSyslog
linux-develOK126
source / vignettesOK202
linux-releaseOK120
macos-releaseOK87
macos-oldrelOK95
windows-develOK82
windows-releaseOK60
windows-oldrelOK73
wasm-releaseOK90

Exports:alternative_gfrpbell_polynomialcheck_lrd_gippcheck_martingale_gfrpcompound_gfcpcov_gippcov_inverse_stablecov_tstfnbpcreate_fcpcreate_gippcreate_tcfcpdgamma_subordinatordtempered_mittag_leffler_levyegf_fractional_bellfde_cgfcpfirst_passage_density_gippfirst_passage_time_fcpfirst_passage_time_gippfirst_passage_time_tcfcpfirst_waiting_time_fcpfirst_waiting_time_tcfcpfractional_bell_polynomialfractional_counting_processfractional_stirling2gamma_subordinatorgeneralized_fractional_risk_processgeneralized_fractional_stirling2generalized_iterated_poissongfcpincomplete_betainverse_stable_subordinatorinvert_pgflt_fcplt_tcfcplt_tempered_mittag_leffler_levylt_tstfnbpmean_cgfcpmean_fcpmean_gfrpmean_gippmean_inverse_stablemean_tcfcpmean_tstfnbpmgamma_subordinatormgf_fcpmgf_gippmittag_lefflermittag_leffler_prabhakarnet_profit_condition_gfrppartial_ordinary_bellpgamma_subordinatorpgf_cgfcppgf_fcppgf_gipppgf_tstfnbppochhammerruin_probability_gfrpsimulate_cgfcpsimulate_fcpsimulate_gfrpsimulate_gippsimulate_tcfcpsimulate_tstfnbpstirling2tempered_mittag_leffler_levytempered_mittag_leffler_momenttempered_st_fnbptempered_stable_subordinatortime_changed_fcpvar_cgfcpvar_fcpvar_gfrpvar_gippvar_tcfcpvar_tstfnbpwright_function

Dependencies:

Readme and manuals

Help Manual

Help pageTopics
Alternative Generalized Fractional Risk Process (AGFRP)alternative_gfrp
Classical Bell Polynomialsbell_polynomial
Check Long-Range Dependence of GIPPcheck_lrd_gipp
Check Martingale Property of GFRPcheck_martingale_gfrp
Compound Generalized Fractional Counting Process (CGFCP)compound_gfcp
Covariance of GIPPcov_gipp
Covariance of Inverse Stable Subordinatorcov_inverse_stable
Covariance of TSTFNBPcov_tstfnbp
Create FCP Objectcreate_fcp
Create GIPP Objectcreate_gipp
Create TCFCP Objectcreate_tcfcp
PDF of Gamma Subordinatordgamma_subordinator
PDF of Tempered Mittag-Leffler Lévy Processdtempered_mittag_leffler_levy
Exponential Generating Function of Fractional Bell Polynomialsegf_fractional_bell
Fractional Differential Equation for CGFCPfde_cgfcp
First Passage Time Density of GIPPfirst_passage_density_gipp
First Passage Time Distribution of FCPfirst_passage_time_fcp
First Passage Time Distribution of GIPPfirst_passage_time_gipp
First Passage Time Distribution of TCFCPfirst_passage_time_tcfcp
First Waiting Time Distribution of FCPfirst_waiting_time_fcp
First Waiting Time Distribution of TCFCPfirst_waiting_time_tcfcp
Fractional Bell Polynomialsfractional_bell_polynomial
Fractional Counting Process (FCP)fractional_counting_process
Fractional Stirling Numbers of the Second Kindfractional_stirling2
Gamma Subordinatorgamma_subordinator
Generalized Fractional Risk Process (GFRP)generalized_fractional_risk_process
Generalized Fractional Stirling Numbers of the Second Kindgeneralized_fractional_stirling2
Generalized Iterated Poisson Process (GIPP)generalized_iterated_poisson
Generalized Fractional Counting Process (GFCP)gfcp
Incomplete Beta Functionincomplete_beta
Inverse Stable Subordinatorinverse_stable_subordinator
Numerical Inversion of Probability Generating Functioninvert_pgf
Laplace Transform of FCPlt_fcp
Laplace Transform of TCFCPlt_tcfcp
Laplace Transform of Tempered Mittag-Leffler Lévy Processlt_tempered_mittag_leffler_levy
Laplace Transform of TSTFNBPlt_tstfnbp
Mean of CGFCPmean_cgfcp
Mean of Fractional Counting Processmean_fcp
Mean of GFRPmean_gfrp
Mean of GIPPmean_gipp
Mean of Inverse Stable Subordinatormean_inverse_stable
Mean of Time-Changed FCPmean_tcfcp
Mean of TSTFNBPmean_tstfnbp
Moment of Gamma Subordinatormgamma_subordinator
Moment Generating Function of FCPmgf_fcp
Moment Generating Function of GIPPmgf_gipp
Mittag-Leffler Functionmittag_leffler
Prabhakar (Three-Parameter) Mittag-Leffler Functionmittag_leffler_prabhakar
Net Profit Condition for GFRPnet_profit_condition_gfrp
Partial Ordinary Bell Polynomialspartial_ordinary_bell
CDF of Gamma Subordinatorpgamma_subordinator
Probability Generating Function of CGFCPpgf_cgfcp
Probability Generating Function of FCPpgf_fcp
Probability Generating Function of GIPPpgf_gipp
Probability Generating Function of TSTFNBPpgf_tstfnbp
Pochhammer Symbolpochhammer
S3 Print Method for FCPprint.fcp
S3 Print Method for GIPPprint.gipp
S3 Print Method for TCFCPprint.tcfcp
Ruin Probability for GFRPruin_probability_gfrp
Simulate Sample Paths of CGFCPsimulate_cgfcp
Simulate Sample Paths of FCPsimulate_fcp
Simulate Sample Paths of GFRPsimulate_gfrp
Simulate Sample Paths of GIPPsimulate_gipp
Simulate Sample Paths of TCFCPsimulate_tcfcp
Simulate Sample Paths of TSTFNBPsimulate_tstfnbp
Classical Stirling Numbers of the Second Kindstirling2
Tempered Mittag-Leffler Lévy Processtempered_mittag_leffler_levy
Fractional Moment of Tempered Mittag-Leffler Lévy Processtempered_mittag_leffler_moment
Tempered Space-Time Fractional Negative Binomial Process (TSTFNBP)tempered_st_fnbp
Tempered Stable Subordinatortempered_stable_subordinator
Time-Changed Fractional Counting Process (TCFCP)time_changed_fcp
Variance of CGFCPvar_cgfcp
Variance of Fractional Counting Processvar_fcp
Variance of GFRPvar_gfrp
Variance of GIPPvar_gipp
Variance of Time-Changed FCPvar_tcfcp
Variance of TSTFNBPvar_tstfnbp
Generalized Wright Functionwright_function