Abhishek Tyagi

Chaudhary Charan Singh University · Department of Statistics

This paper deals with the study of stress-strength model represented by R = P[Y < X < Z] , wherein system failure occurs when the inherent strength X of the system is either lower or higher than the threshold limits of stress (Y or Z). The stress-strength parameter R is studied under progressive type-II censored samples, where the strength. variabl...

In the realm of sustainability, lifetimes are often modeled with discrete measurements due to finite precision, lacking a continuous representation. Despite the inherent continuity in device or patient lifetimes, it is reasonable to consider their observations as stemming from a discretized distribution derived from a continuous model. This study i...

In this chapter, the analysis of the stress-strength reliability of the type \(\Lambda = P\left( {X < Z} \right)\) is considered with progressive Type-II censored data when two independent random variables \(X\) (stress) and \(Z\) (strength) follow a modified form of Lindley distribution. The average amount of time a component can withstand stress...

In this chapter, the parameter estimation of a Burr-Hatke exponential model based on the progressive type-II censored sample is investigated. Various methods of estimation for complete data are generalized to the case under progressive censored samples. These approaches comprise maximum likelihood, least squares, maximum product spacings, and Bayes...

This research focuses on estimating the stress-strength reliability in a system characterized by the influence of two random stresses on its strength, employing both frequentist and Bayesian approaches. The reliability of such systems is represented by the function δ =P(U<V<W), where V denotes the system’s strength, and U and W represent the stress...

The subject matter described herein includes the analysis of the stress-strength reliability of the system, in which the discrete strength of the system is impacted by two random discrete stresses. The reliability function of such systems is denoted by R = P[Y < X < Z], where X is the strength of the system and Y and Z are the stresses. We look at...

In this article, a new discrete distribution called the exponentiated discrete Lindley distribution is derived. The usefulness of this distribution is supported by its ability to analyze different types of count data (over-, under-, equi-dispersed, positively, and negatively skewed). Also, with two parameters, it possesses a bathtub-shaped hazard r...

This paper deals with the classical and Bayesian estimation of the discrete Teissier distribution with randomly censored data. We have obtained the maximum likelihood point and interval estimator for the unknown parameter. Under the squared error loss function, a Bayes estimator is also computed utilising informative and non-informative priors. Fur...

The studies of stress-strength models have garnered substantial interest during the last few decades due to their widespread use in a variety of fields. In this article, we have studied stress-strength reliability \(R = P[Y<Z]\) when stress variable Y strength variable Z follow geometric and Lindley distribution, respectively. Using this stress-str...

In this article, we propose the discrete version of the binomial exponential II distribution for modelling count data. Some of its statistical properties including hazard rate function, mode, moments, skewness, kurtosis, and index of dispersion are derived. The shape of the failure rate function is increasing. Moreover, the proposed model is approp...

In this article, we have developed the discrete version of the continuous inverted Nadarajah-Haghighi distribution and called it a discrete inverted Nadarajah-Haghighi distribution. The present model is well enough to model not only the over-dispersed and positively skewed data but it can also model upside-down bathtub-shaped, decreasing failure ra...

In this article, we have proposed a new continuous model called Modified Topp-Leone distribution. One of the main features of this model is that it has only one parameter but contains varieties of shapes for density and hazard rate functions. We have discussed its various impressive properties like heavy-tailed behavior, mode, moments, quantile, me...

When the load of the failed components within the system shared by the remaining surviving components, the system is called load-sharing system model. The present study deals with the estimation of load-share parameters with Type-I and Type-II failure censored data considering Weibull distribution as the failure time distribution of each component...

This article presents a novel discrete distribution with a single parameter, called the discrete Teissier distribution. It is noted that this model, with one parameter, offers a high degree of fitting flexibility as it is capable of modelling equi-, over-, and under-dispersed, positive and negative skewed, and increasing failure rate datasets. In t...

In this article, we introduce some reliability concepts for the bivariate Pareto Type II distribution including joint hazard rate function, CDF for parallel and series systems, joint mean residual lifetime, and joint vitality function. The maximum likelihood and Bayesian estimation methods are utilized to estimate the model parameters. Simulation i...

In this article, a new one-parameter discrete distribution called discrete Burr-Hatke exponential distribution is introduced and its mathematical characteristics are thoroughly investigated. The proposed distribution is capable of modelling over-dispersed, positively skewed, decreasing failure rate, and randomly right-censored data. We have also in...

In this article, a discrete analogue of continuous Teissier distribution is presented. Its several important distributional characteristics have been derived. The estimation of the unknown parameter has been done using the method of maximum likelihood and the method of moment. Two real data applications have been presented to show the applicability...

In this article, a discrete analogue of continuous Teissier distribution is presented. Its several important distributional characteristics have been derived. The estimation of the unknown parameter has been done using the method of maximum likelihood and the method of moment. Two real data applications have been presented to show the applicability...

In this study, we introduce an extended version of the modified Weibull distribution with an additional shape parameter, in order to provide more flexibility to its density and the hazard rate function. The distribution is capable of modeling the bathtub-shaped, decreasing, increasing and the constant hazard rate function. The proposed model contai...

Linear and circular consecutive models play a vital role to study the mechanical systems emerging in various fields including survival analysis, reliability theory, biological disciplines, and other lifetime sciences. As a result, analysis of reliability properties of consecutive k − out − of − n : F systems has gained a lot of attention in recent...

In the statistical literature, several discrete distributions have been developed so far. However, in this progressive technological era, the data generated from different fields is getting complicated day by day, making it difficult to analyze this real data through the various discrete distributions available in the existing literature. In this c...

In this article, we have proposed a new generalization of the odd Weibull-G family by consolidating two notable families of distributions. We have derived various mathematical properties of the proposed family, including quantile function, skewness, kurtosis, moments, incomplete moments, mean deviation, Bonferroni and Lorenz curves, probability wei...

Recently, the two‐parameter Chen distribution has widely been used for reliability studies in various engineering fields. In this article, we have developed various statistical inferences on the composite dynamic system, assuming Chen distribution as a baseline model. In this dynamic system, failure of a component induces a higher load on the survi...

The studies which dealt with inferential statistics on continuous lifetime models in reference to censored data are widely available in the literature. However, dealing with discrete distributions under censored data is somewhat tricky due to the possibilities of ties in the sample of lifetime observations. Given this fact, the present study addres...

The study deals with the classical and Bayesian estimation of the stress-strength reliability of the form R=P[Y<X<Z] under progressive Type-II censoring scheme, when X, Y, and Z are independent Weibull distributed random variables. In classical setup, we obtain maximum likelihood and uniformly minimum variance unbiased estimator of R. Further, assu...

In load-sharing systems, the components are subjected to share the system workload and if any of the components within the system fails, its load is immediately transfer to the rest of the surviving components, due to which the system working efficiency remains unaffected. The present study addresses the problem of parameter estimation of k-compone...

The discretization of continuous distribution has paramount importance in survival analysis where the lifetime is recorded on a discrete scale. The present study proposes a discrete version of the continuous Perks distribution along with its important distributional and reliability properties. The parameter estimation from the frequentist point of...

When the load of the failed components within the system shared by the remaining surviving components, the system is called load-sharing system model. The present study deals with the estimation of load-share parameters with Type-I and Type-II failure censored data considering Weibull distribution as the failure time distribution of each component...

In this study, we introduce a discrete version of continuous additive Perks–Weibull distribution proposed by Singh (Commun Math Stat 4(4):473–493, 2016), and named as discrete additive Perks–Weibull distribution. This proposed distribution has bathtub-shaped as well as increasing hazard rate, and due to this characteristic it lies in the class of f...