Fit beta calibration models and obtain calibrated probabilities from
    them.

A family of novel beta mixture models (BMMs) has been developed by Majumdar et al. (2022) <doi:10.48550/arXiv.2211.01938> to appositely model the beta-valued cytosine-guanine dinucleotide (CpG) sites, to objectively identify methylation state thresholds and to identify the differentially methylated CpG (DMC) sites using a model-based clustering approach. The family of beta mixture models employs different parameter constraints applicable to different study settings. The EM algorithm is used for parameter estimation, with a novel approximation during the M-step providing tractability and ensuring computational feasibility.

Implements the four-parameter Beta-Danish distribution and its
    three-parameter Exponentiated Danish submodel for survival, reliability
    and lifetime data analysis, following Ahmad and Danish (2025)
    <doi:10.2478/jamsi-2025-0010>. Density, distribution, quantile, survival,
    hazard and random generation functions are evaluated so as to retain
    accuracy in the heavy upper tail, where the survival function is regularly
    varying. Estimation covers maximum likelihood for complete and
    right-censored samples, ridge-penalized fitting for weakly identified
    regimes, a grouped likelihood for times recorded on a coarse grid, and
    Bayesian sampling. Inference provides log-scale Wald and profile
    likelihood intervals, together with a reparameterization in terms of the
    identified composite of the two shape parameters. Structural properties
    include raw, incomplete and conditional moments with their existence
    conditions, Shannon, Renyi and Tsallis entropies, mean residual life,
    mean deviations, Lorenz and Bonferroni curves, probability weighted
    moments, order statistics, stress-strength reliability, hazard shape
    classification and the tail index. Regression modules cover accelerated
    failure time models, mixture and promotion-time cure models, and competing
    risks with Aalen-Johansen comparison and Gray's test. Analyses can be run
    directly from a delimited text file or spreadsheet.