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This paper introduces a new probability distribution called the mixture symmetric gamma (MSG) distribution, which is defined as a mixture of two symmetric gamma distributions. Its statistical properties and applications are explored. We first examine its mathematical properties, including the possible shapes of the corresponding probability density function, as well as the moments, and the moment‐generating function. We then look at parameter estimation using various frequentist and Bayesian methods, such as moment estimation, maximum likelihood method, least‐squares method, and Bayesian approaches. In addition, the prediction of future observations under the MSG model is extensively covered, considering both frequentist and Bayesian perspectives, including median prediction, best unbiased prediction, and Bayesian prediction. A comprehensive simulation study is conducted to evaluate the performance of the proposed estimation and prediction techniques. Finally, the practical applicability of the MSG model is demonstrated through the analysis of four real‐world datasets. It is shown to outperform several well‐known competing models in terms of goodness‐of‐fit. The results highlight the inherent simplicity, efficiency, robustness, and intuitive interpretability of the MSG distribution, making it a compelling choice for modeling data with a symmetric pattern, with potential applications in diverse domains. [ABSTRACT FROM AUTHOR]

A new non-linear stationary process for time series of counts is introduced. The process is composed of the survival and innovation component. The survival component is based on the generalized zero-modified geometric thinning operator, where the innovation process figures in the survival component as well. A few probability distributions for the innovation process have been discussed, in order to adjust the model for observed series with the excess number of zeros. The conditional maximum likelihood and the conditional least squares methods are investigated for the estimation of the model parameters. The practical aspect of the model is presented on some real-life data sets, where we observe data with inflation as well as deflation of zeroes so we can notice how the model can be adjusted with the proper parameter selection. [ABSTRACT FROM AUTHOR]

This paper presents a multiple step-stress accelerated life test using type II censoring. Assuming that the lifetimes of the test item follow the gamma distribution, the maximum likelihood estimation and Bayesian approaches are used to estimate the distribution parameters. In the Bayesian approach, new parametrizations can lead to new prior distributions and can be a useful technique to improve the efficiency and effectiveness of Bayesian modeling, particularly when dealing with complex or high-dimensional models. Therefore, in this paper, we present two sets of prior distributions for the parameters of the accelerated test where one of them is based on the reparametrization of the other. The performance of the proposed prior distributions and maximum likelihood approach are investigated and compared by examining the summaries and frequentist coverage probabilities of intervals. We introduce the Markov Chain Monte Carlo (MCMC) algorithms to generate samples from the posterior distributions in order to evaluate the estimators and intervals. Numerical simulations are conducted to examine the approach's performance and one-sample lifetime data are presented to illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

This paper introduces the Poisson-Lindley minification integer-valued autoregressive (PLMINAR) process, a novel statistical model for analyzing count time series data. The modified negative binomial thinning and the Poisson-Lindley (PL) marginal distribution served as the foundation for the model. The proposed model was examined in terms of its basic stochastic properties, especially related to conditional stochastic measures (e.g., transition probabilities, conditional mean and variance, autocorrelation function). Through comprehensive simulations, the effectiveness of various parameter estimation techniques was validated. The PL-MINAR model's practical utility was demonstrated in analyzing the number of Bitcoin transactions and stock trades, showing its superior or comparable performance to the established INAR model. By offering a robust tool for financial time series analysis, this research holds potential for significant improvements in forecasting and understanding market dynamics. [ABSTRACT FROM AUTHOR]

This paper explores bimodal skew-symmetric distributions, a versatile family of distributions characterized by parameters that control asymmetry and kurtosis. These distributions encapsulate both symmetrical and well-known asymmetrical behaviors. A simulation study evaluates the model's estimation accuracy, detailing the score function and the robustness of the observed information matrix, which is proven to be non-singular under specific conditions. We apply the bimodal skew-normal model to protein data from cancer cells, comparing its performance against four established distributions supported on the entire real line. Results indicate superior performance by the proposed model, underscoring its potential for enhancing analytical precision in biological research. [ABSTRACT FROM AUTHOR]