Indranil Ghosh

The discrete version of the Pareto distribution, popularly known as the Zipf distribution, and its truncated version are not new in the literature but several structural properties have not yet been discussed, and nor has its application to a wide range of observed phenomena. Here, we refer to the truncated Zipf distribution meaning the Zipf distribution when the support set is finite. Several interesting and useful structural properties of the truncated Zipf distribution, such as the modal dominance bounds, recurrence relation among successive raw moments, and stochastic ordering are thoroughly discussed. To exhibit the flexibility of the assumed probability model, COVID-19 datasets from three different geographical regions have been re-analyzed and are compared with several rival univariate discrete probability models which establishes the superiority of the truncated Zipf distribution.

A new approach in constructing a univariate absolutely continuous probability model via power transformation is adopted. The proposed distribution appears to subsume several popular univariate continuous probability models that are already existent in the literature. In addition, the hazard rate function of the proposed distribution appears to possess all possible shapes, increasing, decreasing, and upside-down which is not present in all existing extensions and generalizations of the log-logistic (LL) distribution. Various established estimation strategies under the classical approach such as maximum product spacing, weighted least squares estimation, etc., are adopted to exhibit the flexibility of the proposed probability distribution. The emphasis has been made on the estimation procedure and the new probability model is indeed augmenting the existing literature in many aspects which are highlighted in the simulation and also in the real data application section.

Industry surveys have shown that efforts of thwarting or at least mitigating strategic, operational, and financial risks may not always be adequately aligned: financial risks are given most of the attention, whereas lesser-mitigated strategic and operational risks account for most of a company’s volatility. The novelty of this article lies in the fact that we have made a sincere effort to efficiently estimate the total number of possible risk sources corresponding to three types of risk, namely, financial, operational and strategic. To address the issue of estimation, we have put forward two different approaches for what we call a proportional method, for a more balanced allocation of a company’s risk management priorities and resources by assuming a probability distribution for each of the three types of risk sources and then estimating the number of risk resources using the method of maximum likelihood. In addition, we have also discussed a scenario in which the risk-thwarting probability corresponding to any of three types of risks might be unknown, along with the unknown value of the number of risk sources.

Estimation of the parameters for a bivariate hidden truncated Pareto (type (IV)) models have already been discussed in the literature, see [3, 9, 13] under

This article explores and derives the estimation of the multicomponent stress–strength (MSS) reliability parameter, assuming that the samples are coming from the inverted exponentiated Pareto distribution using a progressively first‐failure censored scheme. To estimate the MSS reliability, both classical and Bayesian approaches are adopted. In the classical approach, the maximum likelihood and the asymptotic confidence interval estimation methods are used. The Bayes estimates with their corresponding highest posterior density credible interval estimates are obtained under the Bayesian approach, under the linear exponential loss function under both the noninformative and gamma informative priors. In addition, to compute the Bayes estimates, Markov chain Monte Carlo methods are used. To compare the efficacy of the different estimation strategies adopted in this paper, a Monte Carlo simulation study is carried out. To demonstrate the applicability of the proposed methodology, two real‐life scenarios resulting/arising from two different carbon fiber data sets are re‐analyzed.

It has been observed that quite often, in health-related studies/clinical trials data, we frequently come across left/right skewed heavy-tailed survival data for which the available probability models from the existing literature are not adequate. In this article, we explore and study a new probability distribution with a bounded domain, namely the Bradford distribution with a single parameter θ, henceforth, in short BF(θ). For this distribution, several tractability advantages (in particular, for modeling medical data) have not been explored, to date, to the best of the knowledge of the author. The BF(θ) distribution represents the advantage of not involving any special function in its formulation. We provide a comprehensive study of general mathematical and statistical properties of this distribution that are desirable traits when fitting clinical trials/health data among many others. The utility of this distribution is highlighted via the application/(re-analysis of) in two different well-known datasets-(i) Arthritis pain relief data, and (ii) Tissue damage dataset for two different objectives. Using information theoretic criteria, we compare the performance of the BF(θ) distribution with several rival probability models defined on the unit interval, such as the beta, Kumaraswamy, bounded-weighted exponential, unit Weibull, and many more. The usefulness of the current paper is manifold, and can be summarized as follows: First, the BF(θ) distribution cannot be obtained via some routine transformation from any of the well-known absolutely continuous univariate random variables, and therefore, it augments the existing literature on statistical distribution theory.The BF(θ) distribution has simple and analytically tractable forms for the associated density and quantile function. Since the quantile function is in a closed form, this distribution can be utilized to model censored data which are an important feature. Specifically, this distribution has a clear advantage over the class of univariate distributions defined on the unit interval and that is, it has only one parameter. Needless to say, the associated inferential measures, such as the MLE (discussed in Section 3), are very easy to implement.Among several existing univariate absolutely continuous probability models, one of the major limitations is that they do not perform satisfactorily well for small samples, because of the presence of two or more model parameters. In contrast, the BF(θ) distribution appears to be working well in the case of small samples (such as for a sample of size 12, see Section 4.2). The above set of arguments warrant for a separate and detailed study for the BF(θ) distribution.

To search for the existence of most nearly compatible probability distributions under the discrete set-up (when the given putative conditional distribution