Reliability analysis of the new exponential inverted topp–leone distribution with applications

The inverted Topp–Leone distribution is a new, appealing model for reliability analysis. In this paper, a new distribution, named new exponential inverted Topp–Leone (NEITL) is presented, which adds an extra shape parameter to the inverted Topp–Leone distribution. The graphical representations of its density, survival, and hazard rate functions are provided. The following properties are explored: quantile function, mixture representation, entropies, moments, and stress– strength reliability. We plotted the skewness and kurtosis measures of the proposed model based on the quantiles. Three different estimation procedures are suggested to estimate the distribution parameters, reliability, and hazard rate functions, along with their confidence intervals. Additionally, stress–strength reliability estimators for the NEITL model were obtained. To illustrate the findings of the paper, two real datasets on engineering and medical fields have been analyzed

Robust Estimation methods of Generalized Exponential Distribution with Outliers

This paper discussed robust estimation for point estimation of the shape and scale parameters for generalized exponential (GE) distribution using a complete dataset in the presence of various percentages of outliers. In the case of outliers, it is known that classical methods such as maximum likelihood estimation (MLE), least square (LS) and maximum product spacing (MPS) in case of outliers cannot reach the best estimator. To confirm this fact, these classical methods were applied to the data of this study and compared with non-classical estimation methods. The non-classical (Robust) methods such as least absolute deviations (LAD), and M-estimation (using M. Huber (MH) weight and M. Bisquare (MB) weight) had been introduced to obtain the best estimation method for the parameters of the GE distribution. The comparison was done numerically by using the Monte Carlo simulation study. The two real datasets application confirmed that the M-estimation method is very much suitable for estimating the GE parameters. We concluded that the M-estimation method using Huber object function is a suitable estimation method in estimating the parameters of the GE distribution for a complete dataset in the presence of various percentages of outliers

Extended Odd Weibull Pareto Distribution, Estimation and Applications

We introduce a new three-parameter continuous lifetime. It combines Pareto and Weibull distributions to formulate the extended odd Weibull Pareto distribution. This new distribution has many nice properties as it has a simple linear representation. We observe its hazard rate function, moments and moment generating function, in addition to mean residual and mean inactivity time. Different classical and Bayesian estimation methods are used to estimate the unknown parameters of extended odd Weibull Pareto distribution. Monte Carlo Markov chain method are used for numerical analysis, simulation is used to assess the use of estimation methods. Two real data examples are analyzed for illustrative purpose

Applying Transformer Insulation Using Weibull Extended Distribution Based on Progressive Censoring Scheme

In this paper, the Weibull extension distribution parameters are estimated under a progressive type-II censoring scheme with random removal. The parameters of the model are estimated using the maximum likelihood method, maximum product spacing, and Bayesian estimation methods. In classical estimation (maximum likelihood method and maximum product spacing), we did use the Newton–Raphson algorithm. The Bayesian estimation is done using the Metropolis–Hastings algorithm based on the square error loss function. The proposed estimation methods are compared using Monte Carlo simulations under a progressive type-II censoring scheme. An empirical study using a real data set of transformer insulation and a simulation study is performed to validate the introduced methods of inference. Based on the result of our study, it can be concluded that the Bayesian method outperforms the maximum likelihood and maximum product-spacing methods for estimating the Weibull extension parameters under a progressive type-II censoring scheme in both simulation and empirical studies

Progressive Type-II Censoring Schemes of Extended Odd Weibull Exponential Distribution with Applications in Medicine and Engineering

In this paper, the parameters of the extended odd Weibull exponential distribution are estimated under progressive type-II censoring scheme with random removal. The model parameters are estimated using the maximum product spacing and maximum likelihood estimation methods. Further, we explore the asymptotic confidence intervals and bootstrap confidence intervals for the model parameters. Monte Carlo simulations are performed to compare between the proposed estimation methods under progressive type-II censoring scheme. An empirical study using two real datasets form engineering and medicine fields to validate the introduced methods of inference. Based on our study, we can conclude that the maximum product of spacing method outperforms the maximum likelihood method for estimating the extended odd Weibull exponential (EOWE) parameters under a progressive type-II censoring scheme in both numerical and empirical cases

Bayesian Estimation of a Transmuted Topp-Leone Length Biased Exponential Model Based on Competing Risk with the Application of Electrical Appliances

Competing risk (CoR) models are frequently disregarded in failure rate analysis, and traditional statistical approaches are used to study the event of interest. In this paper, we proposed a new lifetime distribution by generalizing the length biased exponential (LBE) distribution using the transmuted Topp-Leone-G (TTL-G) family of distributions. The new three parameter model is called the transmuted Topp-Leone length biased exponential (TTLLBE) distribution. A comprehensive account of various mathematical features of the TTLLBE model are derived. The unknown parameters of the proposed distribution are estimated by six classical approaches: the maximum likelihood (ML) approach, maximum product spacing (MPS) approach, least square (LS) approach, Weighted LS (WLS) approach, Cramér-Von Mises (CVN) approach, Anderson–Darling (AD) approach, and Bayesian approach. The stability of the model parameters is examined through the simulation study. The applications of our proposed distribution are explained through real data and its performance is illustrated through its comparison with the competent existing distributions. The TTLLBE model depend on the CoR model has been obtained and estimated parameter of this model by ML and Bayesian estimation approaches. In electrical appliances, we found two main causes of failure, and the data of electrical appliances are fitted to our model. Therefore, we analyzed the TTLLBE model depend on the CoR model to obtain the strong cause of failure

Bayesian Estimation of a Transmuted Topp-Leone Length Biased Exponential Model Based on Competing Risk with the Application of Electrical Appliances

Competing risk (CoR) models are frequently disregarded in failure rate analysis, and traditional statistical approaches are used to study the event of interest. In this paper, we proposed a new lifetime distribution by generalizing the length biased exponential (LBE) distribution using the transmuted Topp-Leone-G (TTL-G) family of distributions. The new three parameter model is called the transmuted Topp-Leone length biased exponential (TTLLBE) distribution. A comprehensive account of various mathematical features of the TTLLBE model are derived. The unknown parameters of the proposed distribution are estimated by six classical approaches: the maximum likelihood (ML) approach, maximum product spacing (MPS) approach, least square (LS) approach, Weighted LS (WLS) approach, Cramér-Von Mises (CVN) approach, Anderson–Darling (AD) approach, and Bayesian approach. The stability of the model parameters is examined through the simulation study. The applications of our proposed distribution are explained through real data and its performance is illustrated through its comparison with the competent existing distributions. The TTLLBE model depend on the CoR model has been obtained and estimated parameter of this model by ML and Bayesian estimation approaches. In electrical appliances, we found two main causes of failure, and the data of electrical appliances are fitted to our model. Therefore, we analyzed the TTLLBE model depend on the CoR model to obtain the strong cause of failure

Reliability Analysis of the New Exponential Inverted Topp–Leone Distribution with Applications

The inverted Topp–Leone distribution is a new, appealing model for reliability analysis. In this paper, a new distribution, named new exponential inverted Topp–Leone (NEITL) is presented, which adds an extra shape parameter to the inverted Topp–Leone distribution. The graphical representations of its density, survival, and hazard rate functions are provided. The following properties are explored: quantile function, mixture representation, entropies, moments, and stress–strength reliability. We plotted the skewness and kurtosis measures of the proposed model based on the quantiles. Three different estimation procedures are suggested to estimate the distribution parameters, reliability, and hazard rate functions, along with their confidence intervals. Additionally, stress–strength reliability estimators for the NEITL model were obtained. To illustrate the findings of the paper, two real datasets on engineering and medical fields have been analyzed

The Weibull Generalized Exponential Distribution with Censored Sample: Estimation and Application on Real Data

This paper is concerned with the estimation of the Weibull generalized exponential distribution (WGED) parameters based on the adaptive Type-II progressive (ATIIP) censored sample. Maximum likelihood estimation (MLE), maximum product spacing (MPS), and Bayesian estimation based on Markov chain Monte Carlo (MCMC) methods have been determined to find the best estimation method. The Monte Carlo simulation is used to compare the three methods of estimation based on the ATIIP-censored sample, and also, we made a bootstrap confidence interval estimation. We will analyze data related to the distribution about single carbon fiber and electrical data as real data cases to show how the schemes work in practice