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  "Package": "StochFracPoisson",
  "Title": "Stochastic Poisson Processes and Fractional Counting Models",
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  "Description": "Implementation of advanced stochastic counting processes.\nMain models include the Fractional Counting Process at Levy\ntimes (Garg et al. (2025) <doi:10.1007/s10955-025-03515-9>),\nthe Generalized Iterated Poisson Process (Soni & Pathak (2024)\n<doi:10.1007/s10959-024-01362-0>), the Generalized Fractional\nRisk Process (Soni & Pathak (2024)\n<doi:10.1007/s11009-024-10111-z>), and the Tempered Space-Time\nFractional Negative Binomial Process (Garg et al. (2025)\n<doi:10.1007/s11009-025-10179-1>).",
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  "Author": "Shikhar Tyagi [aut, cre] (ORCID:\n<https://orcid.org/0000-0003-1606-0844>), Vrijesh Tripathi\n[aut]",
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  "Date/Publication": "2026-07-30 18:52:30 UTC",
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    "bell_polynomial",
    "check_lrd_gipp",
    "check_martingale_gfrp",
    "compound_gfcp",
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    "cov_inverse_stable",
    "cov_tstfnbp",
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    "create_tcfcp",
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    "dtempered_mittag_leffler_levy",
    "egf_fractional_bell",
    "fde_cgfcp",
    "first_passage_density_gipp",
    "first_passage_time_fcp",
    "first_passage_time_gipp",
    "first_passage_time_tcfcp",
    "first_waiting_time_fcp",
    "first_waiting_time_tcfcp",
    "fractional_bell_polynomial",
    "fractional_counting_process",
    "fractional_stirling2",
    "gamma_subordinator",
    "generalized_fractional_risk_process",
    "generalized_fractional_stirling2",
    "generalized_iterated_poisson",
    "gfcp",
    "incomplete_beta",
    "inverse_stable_subordinator",
    "invert_pgf",
    "lt_fcp",
    "lt_tcfcp",
    "lt_tempered_mittag_leffler_levy",
    "lt_tstfnbp",
    "mean_cgfcp",
    "mean_fcp",
    "mean_gfrp",
    "mean_gipp",
    "mean_inverse_stable",
    "mean_tcfcp",
    "mean_tstfnbp",
    "mgamma_subordinator",
    "mgf_fcp",
    "mgf_gipp",
    "mittag_leffler",
    "mittag_leffler_prabhakar",
    "net_profit_condition_gfrp",
    "partial_ordinary_bell",
    "pgamma_subordinator",
    "pgf_cgfcp",
    "pgf_fcp",
    "pgf_gipp",
    "pgf_tstfnbp",
    "pochhammer",
    "ruin_probability_gfrp",
    "simulate_cgfcp",
    "simulate_fcp",
    "simulate_gfrp",
    "simulate_gipp",
    "simulate_tcfcp",
    "simulate_tstfnbp",
    "stirling2",
    "tempered_mittag_leffler_levy",
    "tempered_mittag_leffler_moment",
    "tempered_st_fnbp",
    "tempered_stable_subordinator",
    "time_changed_fcp",
    "var_cgfcp",
    "var_fcp",
    "var_gfrp",
    "var_gipp",
    "var_tcfcp",
    "var_tstfnbp",
    "wright_function"
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    {
      "page": "alternative_gfrp",
      "title": "Alternative Generalized Fractional Risk Process (AGFRP)",
      "topics": [
        "alternative_gfrp"
      ]
    },
    {
      "page": "bell_polynomial",
      "title": "Classical Bell Polynomials",
      "topics": [
        "bell_polynomial"
      ]
    },
    {
      "page": "check_lrd_gipp",
      "title": "Check Long-Range Dependence of GIPP",
      "topics": [
        "check_lrd_gipp"
      ]
    },
    {
      "page": "check_martingale_gfrp",
      "title": "Check Martingale Property of GFRP",
      "topics": [
        "check_martingale_gfrp"
      ]
    },
    {
      "page": "compound_gfcp",
      "title": "Compound Generalized Fractional Counting Process (CGFCP)",
      "topics": [
        "compound_gfcp"
      ]
    },
    {
      "page": "cov_gipp",
      "title": "Covariance of GIPP",
      "topics": [
        "cov_gipp"
      ]
    },
    {
      "page": "cov_inverse_stable",
      "title": "Covariance of Inverse Stable Subordinator",
      "topics": [
        "cov_inverse_stable"
      ]
    },
    {
      "page": "cov_tstfnbp",
      "title": "Covariance of TSTFNBP",
      "topics": [
        "cov_tstfnbp"
      ]
    },
    {
      "page": "create_fcp",
      "title": "Create FCP Object",
      "topics": [
        "create_fcp"
      ]
    },
    {
      "page": "create_gipp",
      "title": "Create GIPP Object",
      "topics": [
        "create_gipp"
      ]
    },
    {
      "page": "create_tcfcp",
      "title": "Create TCFCP Object",
      "topics": [
        "create_tcfcp"
      ]
    },
    {
      "page": "dgamma_subordinator",
      "title": "PDF of Gamma Subordinator",
      "topics": [
        "dgamma_subordinator"
      ]
    },
    {
      "page": "dtempered_mittag_leffler_levy",
      "title": "PDF of Tempered Mittag-Leffler Lévy Process",
      "topics": [
        "dtempered_mittag_leffler_levy"
      ]
    },
    {
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      "title": "Exponential Generating Function of Fractional Bell Polynomials",
      "topics": [
        "egf_fractional_bell"
      ]
    },
    {
      "page": "fde_cgfcp",
      "title": "Fractional Differential Equation for CGFCP",
      "topics": [
        "fde_cgfcp"
      ]
    },
    {
      "page": "first_passage_density_gipp",
      "title": "First Passage Time Density of GIPP",
      "topics": [
        "first_passage_density_gipp"
      ]
    },
    {
      "page": "first_passage_time_fcp",
      "title": "First Passage Time Distribution of FCP",
      "topics": [
        "first_passage_time_fcp"
      ]
    },
    {
      "page": "first_passage_time_gipp",
      "title": "First Passage Time Distribution of GIPP",
      "topics": [
        "first_passage_time_gipp"
      ]
    },
    {
      "page": "first_passage_time_tcfcp",
      "title": "First Passage Time Distribution of TCFCP",
      "topics": [
        "first_passage_time_tcfcp"
      ]
    },
    {
      "page": "first_waiting_time_fcp",
      "title": "First Waiting Time Distribution of FCP",
      "topics": [
        "first_waiting_time_fcp"
      ]
    },
    {
      "page": "first_waiting_time_tcfcp",
      "title": "First Waiting Time Distribution of TCFCP",
      "topics": [
        "first_waiting_time_tcfcp"
      ]
    },
    {
      "page": "fractional_bell_polynomial",
      "title": "Fractional Bell Polynomials",
      "topics": [
        "fractional_bell_polynomial"
      ]
    },
    {
      "page": "fractional_counting_process",
      "title": "Fractional Counting Process (FCP)",
      "topics": [
        "fractional_counting_process"
      ]
    },
    {
      "page": "fractional_stirling2",
      "title": "Fractional Stirling Numbers of the Second Kind",
      "topics": [
        "fractional_stirling2"
      ]
    },
    {
      "page": "gamma_subordinator",
      "title": "Gamma Subordinator",
      "topics": [
        "gamma_subordinator"
      ]
    },
    {
      "page": "generalized_fractional_risk_process",
      "title": "Generalized Fractional Risk Process (GFRP)",
      "topics": [
        "generalized_fractional_risk_process"
      ]
    },
    {
      "page": "generalized_fractional_stirling2",
      "title": "Generalized Fractional Stirling Numbers of the Second Kind",
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        "generalized_fractional_stirling2"
      ]
    },
    {
      "page": "generalized_iterated_poisson",
      "title": "Generalized Iterated Poisson Process (GIPP)",
      "topics": [
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      ]
    },
    {
      "page": "gfcp",
      "title": "Generalized Fractional Counting Process (GFCP)",
      "topics": [
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      ]
    },
    {
      "page": "incomplete_beta",
      "title": "Incomplete Beta Function",
      "topics": [
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      ]
    },
    {
      "page": "inverse_stable_subordinator",
      "title": "Inverse Stable Subordinator",
      "topics": [
        "inverse_stable_subordinator"
      ]
    },
    {
      "page": "invert_pgf",
      "title": "Numerical Inversion of Probability Generating Function",
      "topics": [
        "invert_pgf"
      ]
    },
    {
      "page": "lt_fcp",
      "title": "Laplace Transform of FCP",
      "topics": [
        "lt_fcp"
      ]
    },
    {
      "page": "lt_tcfcp",
      "title": "Laplace Transform of TCFCP",
      "topics": [
        "lt_tcfcp"
      ]
    },
    {
      "page": "lt_tempered_mittag_leffler_levy",
      "title": "Laplace Transform of Tempered Mittag-Leffler Lévy Process",
      "topics": [
        "lt_tempered_mittag_leffler_levy"
      ]
    },
    {
      "page": "lt_tstfnbp",
      "title": "Laplace Transform of TSTFNBP",
      "topics": [
        "lt_tstfnbp"
      ]
    },
    {
      "page": "mean_cgfcp",
      "title": "Mean of CGFCP",
      "topics": [
        "mean_cgfcp"
      ]
    },
    {
      "page": "mean_fcp",
      "title": "Mean of Fractional Counting Process",
      "topics": [
        "mean_fcp"
      ]
    },
    {
      "page": "mean_gfrp",
      "title": "Mean of GFRP",
      "topics": [
        "mean_gfrp"
      ]
    },
    {
      "page": "mean_gipp",
      "title": "Mean of GIPP",
      "topics": [
        "mean_gipp"
      ]
    },
    {
      "page": "mean_inverse_stable",
      "title": "Mean of Inverse Stable Subordinator",
      "topics": [
        "mean_inverse_stable"
      ]
    },
    {
      "page": "mean_tcfcp",
      "title": "Mean of Time-Changed FCP",
      "topics": [
        "mean_tcfcp"
      ]
    },
    {
      "page": "mean_tstfnbp",
      "title": "Mean of TSTFNBP",
      "topics": [
        "mean_tstfnbp"
      ]
    },
    {
      "page": "mgamma_subordinator",
      "title": "Moment of Gamma Subordinator",
      "topics": [
        "mgamma_subordinator"
      ]
    },
    {
      "page": "mgf_fcp",
      "title": "Moment Generating Function of FCP",
      "topics": [
        "mgf_fcp"
      ]
    },
    {
      "page": "mgf_gipp",
      "title": "Moment Generating Function of GIPP",
      "topics": [
        "mgf_gipp"
      ]
    },
    {
      "page": "mittag_leffler",
      "title": "Mittag-Leffler Function",
      "topics": [
        "mittag_leffler"
      ]
    },
    {
      "page": "mittag_leffler_prabhakar",
      "title": "Prabhakar (Three-Parameter) Mittag-Leffler Function",
      "topics": [
        "mittag_leffler_prabhakar"
      ]
    },
    {
      "page": "net_profit_condition_gfrp",
      "title": "Net Profit Condition for GFRP",
      "topics": [
        "net_profit_condition_gfrp"
      ]
    },
    {
      "page": "partial_ordinary_bell",
      "title": "Partial Ordinary Bell Polynomials",
      "topics": [
        "partial_ordinary_bell"
      ]
    },
    {
      "page": "pgamma_subordinator",
      "title": "CDF of Gamma Subordinator",
      "topics": [
        "pgamma_subordinator"
      ]
    },
    {
      "page": "pgf_cgfcp",
      "title": "Probability Generating Function of CGFCP",
      "topics": [
        "pgf_cgfcp"
      ]
    },
    {
      "page": "pgf_fcp",
      "title": "Probability Generating Function of FCP",
      "topics": [
        "pgf_fcp"
      ]
    },
    {
      "page": "pgf_gipp",
      "title": "Probability Generating Function of GIPP",
      "topics": [
        "pgf_gipp"
      ]
    },
    {
      "page": "pgf_tstfnbp",
      "title": "Probability Generating Function of TSTFNBP",
      "topics": [
        "pgf_tstfnbp"
      ]
    },
    {
      "page": "pochhammer",
      "title": "Pochhammer Symbol",
      "topics": [
        "pochhammer"
      ]
    },
    {
      "page": "print.fcp",
      "title": "S3 Print Method for FCP",
      "topics": [
        "print.fcp"
      ]
    },
    {
      "page": "print.gipp",
      "title": "S3 Print Method for GIPP",
      "topics": [
        "print.gipp"
      ]
    },
    {
      "page": "print.tcfcp",
      "title": "S3 Print Method for TCFCP",
      "topics": [
        "print.tcfcp"
      ]
    },
    {
      "page": "ruin_probability_gfrp",
      "title": "Ruin Probability for GFRP",
      "topics": [
        "ruin_probability_gfrp"
      ]
    },
    {
      "page": "simulate_cgfcp",
      "title": "Simulate Sample Paths of CGFCP",
      "topics": [
        "simulate_cgfcp"
      ]
    },
    {
      "page": "simulate_fcp",
      "title": "Simulate Sample Paths of FCP",
      "topics": [
        "simulate_fcp"
      ]
    },
    {
      "page": "simulate_gfrp",
      "title": "Simulate Sample Paths of GFRP",
      "topics": [
        "simulate_gfrp"
      ]
    },
    {
      "page": "simulate_gipp",
      "title": "Simulate Sample Paths of GIPP",
      "topics": [
        "simulate_gipp"
      ]
    },
    {
      "page": "simulate_tcfcp",
      "title": "Simulate Sample Paths of TCFCP",
      "topics": [
        "simulate_tcfcp"
      ]
    },
    {
      "page": "simulate_tstfnbp",
      "title": "Simulate Sample Paths of TSTFNBP",
      "topics": [
        "simulate_tstfnbp"
      ]
    },
    {
      "page": "stirling2",
      "title": "Classical Stirling Numbers of the Second Kind",
      "topics": [
        "stirling2"
      ]
    },
    {
      "page": "tempered_mittag_leffler_levy",
      "title": "Tempered Mittag-Leffler Lévy Process",
      "topics": [
        "tempered_mittag_leffler_levy"
      ]
    },
    {
      "page": "tempered_mittag_leffler_moment",
      "title": "Fractional Moment of Tempered Mittag-Leffler Lévy Process",
      "topics": [
        "tempered_mittag_leffler_moment"
      ]
    },
    {
      "page": "tempered_st_fnbp",
      "title": "Tempered Space-Time Fractional Negative Binomial Process (TSTFNBP)",
      "topics": [
        "tempered_st_fnbp"
      ]
    },
    {
      "page": "tempered_stable_subordinator",
      "title": "Tempered Stable Subordinator",
      "topics": [
        "tempered_stable_subordinator"
      ]
    },
    {
      "page": "time_changed_fcp",
      "title": "Time-Changed Fractional Counting Process (TCFCP)",
      "topics": [
        "time_changed_fcp"
      ]
    },
    {
      "page": "var_cgfcp",
      "title": "Variance of CGFCP",
      "topics": [
        "var_cgfcp"
      ]
    },
    {
      "page": "var_fcp",
      "title": "Variance of Fractional Counting Process",
      "topics": [
        "var_fcp"
      ]
    },
    {
      "page": "var_gfrp",
      "title": "Variance of GFRP",
      "topics": [
        "var_gfrp"
      ]
    },
    {
      "page": "var_gipp",
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