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  "Title": "The Beta-Danish Distribution for Lifetime Data Analysis",
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  "Description": "Implements the four-parameter Beta-Danish distribution and\nits three-parameter submodel for survival and reliability\nanalysis, based on Ahmad and Danish (2025)\n<doi:10.2478/jamsi-2025-0010>. Provides functions for density,\ndistribution, quantile, hazard, and random generation. Includes\nmaximum likelihood estimation for complete and right-censored\ndata, goodness-of-fit assessment, comparison with standard\nlifetime distributions, and publication-quality visualizations.\nAdvanced modules support Accelerated Failure Time (AFT)\nregression, mixture and promotion-time cure models, and\ncompeting risks analysis.",
  "URL": "https://bilal-aiou.github.io/BetaDanish/,\nhttps://github.com/bilal-aiou/BetaDanish",
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  "License": "GPL-3",
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  "Date/Publication": "2026-06-04 06:29:00 UTC",
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    "bayes_betadanish",
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    "bd_order_stat_pdf",
    "cif_betadanish",
    "cif_compare",
    "compare_distributions",
    "compare_models",
    "dbetadanish",
    "fit_bd_aft",
    "fit_bd_competing",
    "fit_bd_cure",
    "fit_betadanish",
    "gof_betadanish",
    "hbetadanish",
    "pbetadanish",
    "qbetadanish",
    "rbetadanish",
    "read_survival_data",
    "report_betadanish",
    "simulate_bd_cure_data",
    "simulate_bd_data"
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      "class": [
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      "fields": [
        "time",
        "status"
      ],
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      "table": true,
      "tojson": true
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      "object": "brain_cancer",
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      ],
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        "Gender",
        "Age",
        "Area",
        "FH",
        "CMH",
        "Grade",
        "Surgery",
        "Radiotherapy",
        "Chemotherapy",
        "Treatment",
        "Morphology",
        "Survstatus",
        "Survtime",
        "Types",
        "Morphology1"
      ],
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      "table": true,
      "tojson": true
    },
    {
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      "title": "Breaking Stress of Carbon Fibres",
      "object": "carbon_fibres",
      "class": [
        "data.frame"
      ],
      "fields": [
        "time",
        "status"
      ],
      "rows": 100,
      "table": true,
      "tojson": true
    },
    {
      "name": "leukemia",
      "title": "Acute Myelogenous Leukemia Survival",
      "object": "leukemia",
      "class": [
        "data.frame"
      ],
      "fields": [
        "time",
        "status",
        "group"
      ],
      "rows": 23,
      "table": true,
      "tojson": true
    },
    {
      "name": "melanoma",
      "title": "Malignant Melanoma Survival After Surgery",
      "object": "melanoma",
      "class": [
        "data.frame"
      ],
      "fields": [
        "time",
        "status",
        "sex",
        "age",
        "year",
        "thickness",
        "ulcer"
      ],
      "rows": 205,
      "table": true,
      "tojson": true
    },
    {
      "name": "remission",
      "title": "Bladder Cancer Remission Times",
      "object": "remission",
      "class": [
        "data.frame"
      ],
      "fields": [
        "time",
        "status"
      ],
      "rows": 128,
      "table": true,
      "tojson": true
    },
    {
      "name": "transplant",
      "title": "Bone Marrow Transplant Survival",
      "object": "transplant",
      "class": [
        "data.frame"
      ],
      "fields": [
        "time",
        "status",
        "group"
      ],
      "rows": 91,
      "table": true,
      "tojson": true
    }
  ],
  "_help": [
    {
      "page": "aarset",
      "title": "Aarset Device Failure Times",
      "topics": [
        "aarset"
      ]
    },
    {
      "page": "analyze_betadanish",
      "title": "Comprehensive Beta-Danish Analysis Pipeline",
      "topics": [
        "analyze_betadanish"
      ]
    },
    {
      "page": "bayes_betadanish",
      "title": "Bayesian Estimation for the Beta-Danish Distribution",
      "topics": [
        "bayes_betadanish"
      ]
    },
    {
      "page": "bd_entropy_shannon",
      "title": "Shannon Entropy of the Beta-Danish Distribution",
      "topics": [
        "bd_entropy_shannon"
      ]
    },
    {
      "page": "bd_order_stat_pdf",
      "title": "Density of the r-th Order Statistic",
      "topics": [
        "bd_order_stat_pdf"
      ]
    },
    {
      "page": "BetaDanish",
      "title": "The Beta-Danish Distribution",
      "topics": [
        "BetaDanish",
        "dbetadanish",
        "hbetadanish",
        "pbetadanish",
        "qbetadanish",
        "rbetadanish"
      ]
    },
    {
      "page": "brain_cancer",
      "title": "Brain Cancer Survival Data",
      "topics": [
        "brain_cancer"
      ]
    },
    {
      "page": "carbon_fibres",
      "title": "Breaking Stress of Carbon Fibres",
      "topics": [
        "carbon_fibres"
      ]
    },
    {
      "page": "cif_betadanish",
      "title": "Compute Cumulative Incidence Function (CIF)",
      "topics": [
        "cif_betadanish"
      ]
    },
    {
      "page": "cif_compare",
      "title": "Compare Model-Based CIF to the Aalen-Johansen Estimator",
      "topics": [
        "cif_compare"
      ]
    },
    {
      "page": "coef.betadanish",
      "title": "Extract Coefficients",
      "topics": [
        "coef.betadanish"
      ]
    },
    {
      "page": "compare_distributions",
      "title": "Compare Beta-Danish with Standard Distributions",
      "topics": [
        "compare_distributions"
      ]
    },
    {
      "page": "compare_models",
      "title": "Compare Nested Beta-Danish Models",
      "topics": [
        "compare_models"
      ]
    },
    {
      "page": "fit_bd_aft",
      "title": "Fit Beta-Danish AFT Regression Model",
      "topics": [
        "fit_bd_aft"
      ]
    },
    {
      "page": "fit_bd_competing",
      "title": "Fit Beta-Danish Competing Risks Model",
      "topics": [
        "fit_bd_competing"
      ]
    },
    {
      "page": "fit_bd_cure",
      "title": "Fit Beta-Danish Cure Models",
      "topics": [
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      ]
    },
    {
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      "title": "Fit the Beta-Danish Distribution to Survival Data",
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        "fit_betadanish"
      ]
    },
    {
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      "title": "Goodness-of-Fit Statistics for Beta-Danish Models",
      "topics": [
        "gof_betadanish"
      ]
    },
    {
      "page": "leukemia",
      "title": "Acute Myelogenous Leukemia Survival",
      "topics": [
        "leukemia"
      ]
    },
    {
      "page": "logLik.betadanish",
      "title": "Extract Log-Likelihood",
      "topics": [
        "logLik.betadanish"
      ]
    },
    {
      "page": "melanoma",
      "title": "Malignant Melanoma Survival After Surgery",
      "topics": [
        "melanoma"
      ]
    },
    {
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      "title": "Cox-Snell Residual Plot for AFT and Cure Fits",
      "topics": [
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        "plot.bd_cure"
      ]
    },
    {
      "page": "plot.betadanish",
      "title": "Plot Diagnostics for Beta-Danish Fit",
      "topics": [
        "plot.betadanish"
      ]
    },
    {
      "page": "print.betadanish",
      "title": "Print Method for Beta-Danish Fit",
      "topics": [
        "print.betadanish"
      ]
    },
    {
      "page": "print.summary.betadanish",
      "title": "Print Summary Method for Beta-Danish Fit",
      "topics": [
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    },
    {
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      "title": "Read and Prepare Survival Data",
      "topics": [
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      ]
    },
    {
      "page": "remission",
      "title": "Bladder Cancer Remission Times",
      "topics": [
        "remission"
      ]
    },
    {
      "page": "report_betadanish",
      "title": "Create a compact report from a BetaDanish model fit",
      "topics": [
        "report_betadanish"
      ]
    },
    {
      "page": "simulate_bd_cure_data",
      "title": "Simulate Beta-Danish Cure Data",
      "topics": [
        "simulate_bd_cure_data"
      ]
    },
    {
      "page": "simulate_bd_data",
      "title": "Simulate Data from the Beta-Danish Distribution",
      "topics": [
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    {
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      "title": "Summary Method for Beta-Danish Fit",
      "topics": [
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    },
    {
      "page": "transplant",
      "title": "Bone Marrow Transplant Survival",
      "topics": [
        "transplant"
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    },
    {
      "page": "vcov.betadanish",
      "title": "Extract Variance-Covariance Matrix",
      "topics": [
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        "2. Theoretical Background",
        "The 3-Parameter Submodel",
        "3. Core Distribution Functions",
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        "Example 1: Uncensored Data (Bladder Cancer Remission)",
        "Example 2: Right-Censored Data (Bone Marrow Transplant)",
        "5. Advanced Modeling: Cure Rates",
        "6. Automated Benchmarking",
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