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In this article, a new three-parameter lifetime model called the Gull alpha power exponentiated exponential (GAPEE) distribution is introduced and studied by combining the Gull alpha power family of distributions and the exponentiated exponential distribution. The shapes of the probability density function (PDF) for the GAPEE distribution can be asymmetric shapes, like unimodal, decreasing, and right-skewed. In addition, the shapes of the hazard rate function (hrf) for the GAPEE distribution can be increasing, decreasing, and upside-down shaped. Several statistical features of the GAPEE distribution are computed. Eight estimation methods such as the maximum likelihood, Anderson-Darling, right-tail Anderson-Darling, left-tailed Anderson-Darling, Cramer-von Mises, least-squares, weighted least-squares, and maximum product of spacing are discussed to estimate the parameters of the GAPEE distribution. The flexibility and the importance of the GAPEE distribution were demonstrated utilizing three real-world datasets related to medical sciences. The GAPEE distribution is extremely adaptable and outperforms several well-known statistical models. A bivariate step-stress accelerated life test based on progressive type-I censoring using the model is presented. Minimizing the asymptotic variance of the maximum likelihood estimate of the log of the scale parameter at design stress under progressive type-I censoring yields an expression for the ideal test plan under progressive type-I censoring. [ABSTRACT FROM AUTHOR]

In this article, we intend to introduce and study a new two-parameter distribution as a new extension of the power Topp–Leone (PTL) distribution called the Kavya–Manoharan PTL (KMPTL) distribution. Several mathematical and statistical features of the KMPTL distribution, such as the quantile function, moments, generating function, and incomplete moments, are calculated. Some measures of entropy are investigated. The cumulative residual Rényi entropy (CRRE) is calculated. To estimate the parameters of the KMPTL distribution, both maximum likelihood and Bayesian estimation methods are used under simple random sample (SRS) and ranked set sampling (RSS). The simulation study was performed to be able to verify the model parameters of the KMPTL distribution using SRS and RSS to demonstrate that RSS is more efficient than SRS. We demonstrated that the KMPTL distribution has more flexibility than the PTL distribution and the other nine competitive statistical distributions: PTL, unit-Gompertz, unit-Lindley, Topp–Leone, unit generalized log Burr XII, unit exponential Pareto, Kumaraswamy, beta, Marshall-Olkin Kumaraswamy distributions employing two real-world datasets. [ABSTRACT FROM AUTHOR]

Finite mixture models have several applications in many fields such as statistics, economics, marking, medicine and reliability analysis. In this paper, we obtain the maximum likelihood estimates of the parameters of the mixture of two one-parameter Lindley distributions by using two types of data namely; classified and unclassified samples. Next, we estimate the linear discriminant function of the underlying mixture model and calculate the total probabilities of misclassification as well as the percentage bias through a series of simulation experiments and some real data sets. Consequently, we study the problem of updating the discriminant function on the basis of data of unknown origin. We consider the updating procedure for the linear discriminant function on the basis of two one-parameter Lindley distributions in situations when the additional observations are mixed or classified. Finally, we study the performance of the updating procedures through some simulation experiments by means of the relative efficiencies. [ABSTRACT FROM AUTHOR]

The main contribution of this paper is is updating a nonlinear discriminant function on the basis of data of unknown origin. Specifically a procedure is developed for updating the nonlinear discriminant function on the basis of two Burr Type III distributions (TBIIID) when the additional observations are mixed or classified. First the nonlinear discriminant function of the assumed model is obtained. Then the total probabilities of misclassification are calculated. In addition a Monte carlo simulation runs are used to compute the relative efficiencies in order to investigate the performance of the developed updating procedures. Finally the results obtained in this paper are illustrated through a real and simulated data set. [ABSTRACT FROM PUBLISHER]

In this article, we propose the finite mixture of two Burr Type-III distributions (MTBIIID). First, we formulate the proposed model with some properties and prove the identifiability property. Next, we obtain the maximum likelihood estimates (MLEs) of the unknown parameters of MTBIIID under classified and unclassified observations. Also, we estimate the nonlinear discriminant function of the underlying model. In addition, we calculate the total probabilities of misclassification as well as the percentage bias. Further, we investigate the performance of the all results through series of the simulation experiments by the means of the relative efficiencies. [ABSTRACT FROM AUTHOR]

This research proposes the Kavya-Manoharan Unit Exponentiated Half Logistic (KM-UEHL) distribution as a novel tool for epidemiological modeling of COVID-19 data. Specifically designed to analyze data constrained to the unit interval, the KM-UEHL distribution builds upon the unit exponentiated half logistic model, making it suitable for various data from COVID-19. The paper emphasizes the KM-UEHL distribution's adaptability by examining its density and hazard rate functions. Its effectiveness is demonstrated in handling the diverse nature of COVID-19 data through these functions. Key characteristics like moments, quantile functions, stress-strength reliability, and entropy measures are also comprehensively investigated. Furthermore, the KM-UEHL distribution is employed for forecasting future COVID-19 data under a progressive Type-II censoring scheme, which acknowledges the time-dependent nature of data collection during outbreaks. The paper presents various methods for constructing prediction intervals for future-order statistics, including maximum likelihood estimation, Bayesian inference (both point and interval estimates), and upper-order statistics approaches. The Metropolis-Hastings and Gibbs sampling procedures are combined to create the Markov chain Monte Carlo simulations because it is mathematically difficult to acquire closed-form solutions for the posterior density function in the Bayesian framework. The theoretical developments are validated with numerical simulations, and the practical applicability of the KM-UEHL distribution is showcased using real-world COVID-19 datasets., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Authors.)