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The coherent systems are basic concepts in reliability theory and survival analysis. They contain as particular cases the popular series, parallel and $k$-ou-of-$n$ systems (order statistics). Many results have been obtained for them by…
We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the…
In this paper we propose a new four-parameters distribution with increasing, decreasing, bathtub-shaped and unimodal failure rate, called as the exponentiated Weibull-Poisson (EWP) distribution. The new distribution arises on a latent…
This study introduces the Exponentiated-Exponential-Pareto-Half Normal Mixture Distribution (EEPHND), a novel hybrid model developed to overcome the limitations of classical distributions in modeling complex real-world data. By compounding…
This paper deals with system with $n$ identical elements and one repairing device. While one element working other ones stay in reserve. The distribution of element working and repairing times are supposed to be exponential. Here we obtain…
The primary objective of this scholarly work is to develop two estimation procedures - maximum likelihood estimator (MLE) and method of trimmed moments (MTM) - for the mean and variance of lognormal insurance payment severity data sets…
For a set of binary response variables, conditional mean models characterize the expected value of a response variable given the others and are popularly applied in longitudinal and network data analyses. The quadratic exponential binary…
We consider the classical problem of learning, with arbitrary accuracy, the natural parameters of a $k$-parameter truncated \textit{minimal} exponential family from i.i.d. samples in a computationally and statistically efficient manner. We…
Ordinary least square (OLS), maximum likelihood (ML) and robust methods are the widely used methods to estimate the parameters of a linear regression model. It is well known that these methods perform well under some distributional…
Most theoretical analysis for lifetime distribution explains origins of specific distribution based on independent failure. We develop a unified framework encompassing different lifetime distribution for failure-coupled network systems. We…
We propose a new approach for estimating the parameters of a probability distribution. It consists on combining two new methods of estimation. The first is based on the definition of a new distance measuring the difference between…
The second-largest order statistic is of special importance in reliability theory since it represents the time to failure of a $2$-out-of-$n$ system. Consider two $2$-out-of-$n$ systems with heterogeneous random lifetimes. The lifetimes are…
Topp Leone q Exponential Distruibution is a continuous model distribution used for modelling lifetime phenomena. In this study, we introduce different estimation methods for the unknown parameters of Topp Leone Exponential(TLE) distribution…
Some improved estimators of the location parameters of several exponential distributions with ordered restriction are derived and compared numerically using Monte Carlo simulations. Note that the two-parameter exponential distribution is…
Parameters defined via General Estimating Equations (GEE) can be estimated by maximizing the Empirical Likelihood (EL). Newey and Smith (2004) have recently shown that this EL estimator exhibits desirable higher-order asymptotic properties,…
Reliability inference based on parametric distributions is an important problem in electrical and mechanical engineering. Most existing methods rely on approximations or bootstrap procedures, which may not perform satisfactorily when data…
The study of probabilistic models for the analysis of complex networks represents a flourishing research field. Among the former, Exponential Random Graphs (ERGs) have gained increasing attention over the years. So far, only linear ERGs…
Exponential families encompass the distributions central to modern machine learning -- softmax, Gaussians, and Boltzmann distributions -- and underlie the theory of variational inference, entropy-regularized reinforcement learning, and…
We show that the number of renewals up to time $t$ exhibits distributional fluctuations as $t\to\infty$ if the underlying lifetimes increase at an exponential rate in a distributional sense. This provides a probabilistic explanation for the…
This paper introduces a new two-parameter distribution, referred to as the Shiha distribution, which provides a flexible model for skewed lifetime data with either heavy or light tails. The proposed distribution is applicable to various…