Work in Software Packages


Contains functions that allow Bayesian meta-analysis (1) with binomial data, counts(y) and total counts (n) or, (2) with user-supplied point estimates and associated variances. Case (1) provides an analysis based on the logit transformation of the sample proportion. This methodology is also appropriate for combining data from sample surveys and related sources. The functions can calculate the corresponding similarity matrix. More details can be found in Cahoy and Sedransk (2023), Cahoy and Sedransk (2022) <doi:10.1007/s42519-018-0027-2>, Evans and Sedransk (2001) <doi:10.1093/biomet/88.3.643>, and Malec and Sedransk (1992) <doi:10.1093/biomet/79.3.593>.


Contains functions that allow Bayesian inference on a parameter of some widely-used exponential models. The functions can generate independent samples from the closed-form posterior distribution using the inverse stable prior. Inverse stable is a non-conjugate prior for a parameter of an exponential subclass of discrete and continuous data distributions (e.g. Poisson, exponential, inverse gamma, double exponential (Laplace), half-normal/half-Gaussian, etc.). The prior class provides flexibility in capturing a wide array of prior beliefs (right-skewed and left-skewed) as modulated by a parameter that is bounded in (0,1). The generated samples can be used to simulate the prior and posterior predictive distributions. More details can be found in Cahoy and Sedransk (2019) <doi:10.1007/s42519-018-0027-2>. The package can also be used as a teaching demo for introductory Bayesian courses.


Tests the hypothesis that variances are homogeneous or not using bootstrap. The procedure uses a variance-based statistic, and is derived from a normal-theory test. The test equivalently expressed the hypothesis as a function of the log contrasts of the population variances. A box-type acceptance region is constructed to test the hypothesis. See Cahoy (2010) <doi:10.1016/j.csda.2010.04.012>.


Implements random number generation, plotting, and estimation algorithms for the two-parameter one-sided and two-sided M-Wright (Mainardi-Wright) family.  The M-Wright distributions naturally generalize the widely used one-sided (Airy and half-normal or half-Gaussian) and symmetric (Airy and Gaussian or normal) models. These are widely studied in time-fractional differential equations. References: Cahoy and Minkabo (2017) <doi:10.3233/MAS-170388>; Cahoy (2012) <doi:10.1007/s00180-011-0269-x>; Cahoy (2012) <doi:10.1080/03610926.2010.543299>; Cahoy (2011); Mainardi, Mura, and Pagnini (2010) <doi:10.1155/2010/104505>


Implements the Mittag-Leffler function, distribution, random variate generation, and estimation. Based on the Laplace-Inversion algorithm by Garrappa, R. (2015) <doi:10.1137/140971191>.