Classification is one of the main areas of machine learning, where the target variable is usually categorical with at least two levels. This study focuses on deducing an optimal cut-off point for continuous outcomes (e.g., predicted probabilities) resulting from binary classifiers. To achieve this aim, the study modified univariate discriminant functions by incorporating the error cost of misclassification penalties involved. By doing so, we can systematically shift the cut-off point within its measurement range till the optimal point is obtained. Extensive simulation studies were conducted to investigate the performance of the proposed method in comparison with existing classification methods under the binary logistic and Bayesian quantile regression frameworks. The simulation results indicate that logistic regression models incorporating the proposed method outperform the existing ordinary logistic regression and Bayesian regression models. We illustrate the proposed method with a practical dataset from the finance industry that assesses default status in home equity.

The generalization of probability distributions has a rich history, with various techniques employed to introduce new families of distributions. One notable approach is the transformed‐transformer (T‐X) method, which has been used by several authors to introduce many of novel probability distributions. In this study, we present the new Lindley‐X class, a novel family of continuous probability distributions, and we introduce some submodels within this framework. Our research involves deriving mathematical expressions for various statistical measures, including moments, the generating function, the quantile function, and Renyi entropy. To estimate the parameters of the new family of distributions, we utilize a range of methods, including maximum likelihood, maximum product spacing, least squares, Cramer‐von Mises, and Anderson–Darling estimations. Furthermore, we illustrate the practical applicability of this new family of distributions through the analysis of real‐life datasets.

Background: Maternal mortality is one of the most devastating and emotionally distressing occurrences that can be experienced by a family or society. The objective of the study was to investigate the risk factors associated with maternal mortality across the various sub‐metros using zero‐inflated models.Methods: The study used secondary data obtained from eight health facilities within Kumasi metropolis from 2018 to 2022. The zero‐inflated negative binomial (ZINB) is useful when dealing with count outcomes that show greater variability than would be expected in a standard Poisson distribution, a phenomenon known as overdispersion.Results: The maternal mortality rates (MMRs) for 2018 to 2022 were 427.53, 385.68, 284.21, 323.74, and 440.78 per 100,000 live births, respectively, in the Kumasi metropolis. The study found unsafe abortion, sepsis, tuberculosis, hemorrhage, and hypertension to be significantly associated with maternal mortality.Conclusion: We recommend a continuous health education campaign to encourage pregnant women to seek prompt medication when they suspect sepsis, hypertension, tuberculosis, and hemorrhage. Also, awareness about the risk associated with unsafe abortions should be promoted.

This paper introduces a new probability model called the modified Gompertz distribution from the base Gompertz distribution by combining its hazard function with first and second degree polynomial (linear and quadratic) functions. The new probability model is found to have more flexible hazard shapes with strictly increasing, strictly decreasing, and bumping behaviors. Properties of the new probability model are derived and discussed. Simulation studies and data fitting are conducted. The modified Gompertz distribution is found to fit better to four datasets as compared to the base Gompertz distribution and also six other models which are Topp‐Leone Gompertz, Generalized Gompertz, Exponentiated Gompertz Exponential, Power Gompertz, Gompertz Ampadu Lomax, and Exponential Generalized Extended Gompertz probability distributions. The modified Gompertz distribution is a contribution to the field of statistical theory, having very interesting shapes of hazard function can have applications to survival, waiting time, and reliability data analyses. Any statistical inference from simulation study and data fitting to real‐world data can possibly lead to new knowledge in applied probability, statistics, and application field such as life science, health, and engineering. Generalization to higher order polynomial functions is recommended for future research. Applications of the models to data from various fields can be studied.

In this paper, we have derived and studied new probability distributions by extending the 2‐dimensional Rayleigh distribution (RD). First, we extend the RD to 3 dimensions and then generalize it to k dimensions for any positive integer k ≥ 3. The distributions are named the 3‐dimensional Rayleigh distribution (3‐DRD) and k‐dimensional Rayleigh distribution (k‐DRD), respectively. For both 3‐DRD and k‐DRD, detailed mathematical and statistical properties including derivations of the corresponding cumulative distribution, probability density, survival, and hazard functions, moments, moment generating functions, mode, skewness, kurtosis, and differential entropy are obtained in closed forms. Parameter estimation is done for both models using the maximum likelihood estimation method and some statistical properties of the estimator are discussed for each case. Interestingly, the commonly known Normal, Rayleigh, Maxwell–Boltzmann, chi‐square, gamma, and Erlang distributions are related to the newly developed extended RDs as special cases. For the 3‐DRD, plots of cumulative distribution, probability density, survival, and hazard functions are exhibited, a simulation study is carried out, and random samples are generated using the standard accept–reject (AR) algorithm to check the efficiency of the maximum likelihood estimates of the parameter. Moreover, the new 3‐DRD model is fitted to one simulated and three real datasets, revealing good performance compared to four existing Rayleigh‐based distributions. This study will contribute new knowledge to the field of applied statistics and probability, and the findings will be used as a basis for future research in the field.

In efficacy and safety studies, a vital research concern is to determine the therapeutic window of a pharmaceutical compound. The approach to finding minimum effective dose and maximum safe dose involves multiple comparisons. Generally, in such a problem, a family‐wise error rate is inherited if multiplicity adjustment is not handled properly. This article without a need for multiplicity adjustment formulates a stepwise confidence interval method to identify a therapeutic window of a pharmaceutical compound when equality of variances cannot be assumed and when ratios of variances are known. This article employed Fieller’s method and obtained individual confidence intervals for the identification of the minimum effective dose and maximum safe dose. A simulation study was performed and the results show that the confidence interval method proposed in this article controls the family‐wise error rate strongly. Power increases whenever the ratio of means increases and decreases against higher clinical relevance margins. The proposed procedure was applied to real data and provided optimum results. It was also observed that as both the ratio of means and the sample sizes increase, power increases accordingly.

The explosion of time series count data with diverse characteristics and features in recent years has led to a proliferation of new analysis models and methods. Significant efforts have been devoted to achieving flexibility capable of handling complex dependence structures, capturing multiple distributional characteristics simultaneously, and addressing nonstationary patterns such as trends, seasonality, or change points. However, it remains a challenge when considering them in the context of long-range dependence. The Lévy-based modeling framework offers a promising tool to meet the requirements of modern data analysis. It enables the modeling of both short-range and long-range serial correlation structures by selecting the kernel set accordingly and accommodates various marginal distributions within the class of infinitely divisible laws. We propose an extension of the basic stationary framework to capture additional marginal properties, such as heavy-tailedness, in both short-term and long-term dependencies, as well as overdispersion and zero inflation in simultaneous modeling. Statistical inference is based on composite pairwise likelihood. The model’s flexibility is illustrated through applications to rainfall data in Guinea from 2008 to 2023, and the number of NSF funding awarded to academic institutions. The proposed model demonstrates remarkable flexibility and versatility, capable of simultaneously capturing overdispersion, zero inflation, and heavy-tailedness in count time series data.