Bayesian and Classical Inference under Type-II Censored Samples of the Extended Inverse Gompertz Distribution with Engineering Applications

In this article, we introduce a new three-parameter distribution called the extended inverse-Gompertz (EIGo) distribution. The implementation of three parameters provides a good reconstruction for some applications. The EIGo distribution can be seen as an extension of the inverted exponential, inverse Gompertz, and generalized inverted exponential distributions. Its failure rate function has an upside-down bathtub shape. Various statistical and reliability properties of the EIGo distribution are discussed. The model parameters are estimated by the maximum-likelihood and Bayesian methods under Type-II censored samples, where the parameters are explained using gamma priors. The performance of the proposed approaches is examined using simulation results. Finally, two real-life engineering data sets are analyzed to illustrate the applicability of the EIGo distribution, showing that it provides better fits than competing inverted models such as inverse-Gompertz, inverse-Weibull, inverse-gamma, generalized inverse-Weibull, exponentiated inverted-Weibull, generalized inverted half-logistic, inverted-Kumaraswamy, inverted Nadarajah–Haghighi, and alpha-power inverse-Weibull distributions.

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Statistical Analysis of a Weibull Extension with Bathtub-Shaped Failure Rate Function

Advances in Statistics ◽

10.1155/2014/304724 ◽

2014 ◽

Vol 2014 ◽

pp. 1-15 ◽

Cited By ~ 4

Author(s):

Ronghua Wang ◽

Naijun Sha ◽

Beiqing Gu ◽

Xiaoling Xu

Keyword(s):

Failure Rate ◽

Rate Function ◽

Estimation Methods ◽

Type Ii ◽

Life Distribution ◽

Parameter Inference ◽

Failure Rate Function ◽

Increasing Failure Rate ◽

Censored Samples ◽

Two Parameter

We consider the parameter inference for a two-parameter life distribution with bathtub-shaped or increasing failure rate function. We present the point and interval estimations for the parameter of interest based on type-II censored samples. Through intensive Monte-Carlo simulations, we assess the performance of the proposed estimation methods by a comparison of precision. Example applications are demonstrated for the efficiency of the methods.

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The exact hypothesis test for the shape parameter of a new two-parameter distribution with the bathtub shape or increasing failure rate function under progressive censoring with random removals

Journal of Statistical Computation and Simulation ◽

10.1080/00949650802110433 ◽

2009 ◽

Vol 79 (8) ◽

pp. 1015-1042 ◽

Cited By ~ 1

Author(s):

Shu-Fei Wu ◽

Chin-Chuan Wu ◽

Huan-Min Lin

Keyword(s):

Failure Rate ◽

Shape Parameter ◽

Hypothesis Test ◽

Rate Function ◽

Parameter Distribution ◽

Progressive Censoring ◽

Failure Rate Function ◽

Increasing Failure Rate ◽

Bathtub Shape ◽

Two Parameter

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New Method for Generating New Families of Distributions

Symmetry ◽

10.3390/sym13040726 ◽

2021 ◽

Vol 13 (4) ◽

pp. 726

Author(s):

Lamya A. Baharith ◽

Wedad H. Aljuhani

Keyword(s):

Exponential Distribution ◽

Real Data ◽

Rate Function ◽

New Method ◽

Likelihood Method ◽

Alpha Power ◽

Unknown Parameters ◽

Failure Rate Function ◽

New Approach ◽

Numerical Studies

This article presents a new method for generating distributions. This method combines two techniques—the transformed—transformer and alpha power transformation approaches—allowing for tremendous flexibility in the resulting distributions. The new approach is applied to introduce the alpha power Weibull—exponential distribution. The density of this distribution can take asymmetric and near-symmetric shapes. Various asymmetric shapes, such as decreasing, increasing, L-shaped, near-symmetrical, and right-skewed shapes, are observed for the related failure rate function, making it more tractable for many modeling applications. Some significant mathematical features of the suggested distribution are determined. Estimates of the unknown parameters of the proposed distribution are obtained using the maximum likelihood method. Furthermore, some numerical studies were carried out, in order to evaluate the estimation performance. Three practical datasets are considered to analyze the usefulness and flexibility of the introduced distribution. The proposed alpha power Weibull–exponential distribution can outperform other well-known distributions, showing its great adaptability in the context of real data analysis.

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Alpha Power Transformed Log-Logistic Distribution with Application to Breaking Stress Data

Advances in Mathematical Physics ◽

10.1155/2020/2193787 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

Maha A. Aldahlan

Keyword(s):

Maximum Likelihood Method ◽

Real Life ◽

Quantile Function ◽

Moment Generating Function ◽

Likelihood Method ◽

Logistic Distribution ◽

Model Parameters ◽

Alpha Power ◽

New Model ◽

Mathematical Properties

In this paper, a new three-parameter lifetime distribution is introduced; the new model is a generalization of the log-logistic (LL) model, and it is called the alpha power transformed log-logistic (APTLL) distribution. The APTLL distribution is more flexible than some generalizations of log-logistic distribution. We derived some mathematical properties including moments, moment-generating function, quantile function, Rényi entropy, and order statistics of the new model. The model parameters are estimated using maximum likelihood method of estimation. The simulation study is performed to investigate the effectiveness of the estimates. Finally, we used one real-life dataset to show the flexibility of the APTLL distribution.

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A new Weibull Exponentiated Inverted Weibull Distribution for modelling positively-skewed data

Global Journal of Pure and Applied Sciences ◽

10.4314/gjpas.v27i1.6 ◽

2021 ◽

Vol 27 (1) ◽

pp. 43-53

Author(s):

J.O. Braimah ◽

J.A. Adjekukor ◽

N. Edike ◽

S.O. Elakhe

Keyword(s):

Weibull Distribution ◽

Failure Rate ◽

Real Life ◽

Rate Function ◽

Likelihood Method ◽

Estimation Of Parameters ◽

Failure Rate Function ◽

Lifetime Distributions ◽

Increasing Failure Rate ◽

Modeling Data

An Exponentiated Inverted Weibull Distribution (EIWD) has a hazard rate (failure rate) function that is unimodal, thus making it less efficient for modeling data with an increasing failure rate (IFR). Hence, the need to generalize the EIWD in order to obtain a distribution that will be proficient in modeling these types of dataset (data with an increasing failure rate). This paper therefore, extends the EIWD in order to obtain Weibull Exponentiated Inverted Weibull (WEIW) distribution using the Weibull-Generator technique. Some of the properties investigated include the mean, variance, median, moments, quantile and moment generating functions. The explicit expressions were derived for the order statistics and hazard/failure rate function. The estimation of parameters was derived using the maximum likelihood method. The developed model was applied to a real-life dataset and compared with some existing competing lifetime distributions. The result revealed that the (WEIW) distribution provided a better fit to the real life dataset than the existing Weibull/Exponential family distributions.

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Estimation procedures on Type-II censored data from a scaled Muth distribution

Sigma Journal of Engineering and Natural Sciences – Sigma Mühendislik ve Fen Bilimleri Dergisi ◽

10.14744/sigma.2021.00004 ◽

2021 ◽

pp. 148-158

Author(s):

Hayrinisa Demirci BIÇER

Keyword(s):

Censored Data ◽

Mean Squared Error ◽

Real Life ◽

Model Parameters ◽

Type Ii ◽

Monte Carlo Simulation Study ◽

Anal Ysis ◽

Squared Error ◽

Type Ii Censored Data ◽

Censoring Scheme

In the present paper, we consider the estimation problem for the scaled Muth distribution under Type-II censoring scheme. In order to estimate the model parameters α and β, the maximum likelihood, the least-squares, and the maximum spacing estimators are derived. To show estimation efficiencies of the estimators obtained with this paper, we present an exten- sive Monte-Carlo simulation study in which the estimators are compared according to bias and mean squared error criteria. Furthermore, we evaluate the applicability of the scaled Muth distribution by taking into account both full and Type-II censored data situations by an anal- ysis conducted on a real-life dataset.

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A Generalization of Binomial Exponential-2 Distribution: Copula, Properties and Applications

Symmetry ◽

10.3390/sym12081338 ◽

2020 ◽

Vol 12 (8) ◽

pp. 1338

Author(s):

Naif Alotaibi ◽

Igor V. Malyk

Keyword(s):

Residual Life ◽

Real Life ◽

Real Data ◽

Moment Generating Function ◽

Likelihood Method ◽

Model Parameters ◽

Simple Type ◽

Conditional Moment ◽

Failure Rate Function ◽

New Model

In this paper, we propose a new three-parameter lifetime distribution for modeling symmetric real-life data sets. A simple-type Copula-based construction is presented to derive many bivariate- and multivariate-type distributions. The failure rate function of the new model can be “monotonically asymmetric increasing”, “increasing-constant”, “monotonically asymmetric decreasing” and “upside-down-constant” shaped. We investigate some of mathematical symmetric/asymmetric properties such as the ordinary moments, moment generating function, conditional moment, residual life and reversed residual functions. Bonferroni and Lorenz curves and mean deviations are discussed. The maximum likelihood method is used to estimate the model parameters. Finally, we illustrate the importance of the new model by the study of real data applications to show the flexibility and potentiality of the new model. The kernel density estimation and box plots are used for exploring the symmetry of the used data.

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A further extension of the generalized burn-in model

Journal of Applied Probability ◽

10.1239/jap/1044476840 ◽

2003 ◽

Vol 40 (1) ◽

pp. 264-270 ◽

Cited By ~ 29

Author(s):

Ji Hwan Cha

Keyword(s):

Probability Function ◽

Rate Function ◽

Replacement Policy ◽

Time Dependent ◽

Type Ii ◽

Failure Rate Function ◽

Mild Conditions ◽

Optimal Replacement ◽

Replacement Model ◽

Optimal Replacement Policy

In this paper, the generalized burn-in and replacement model considered by Cha (2001) is further extended to the case in which the probability of Type II failure is time dependent. Two burn-in procedures are considered and they are compared in cases when both the procedures are applicable. Under some mild conditions on the failure rate function r(t) and the Type II failure probability function p(t), the problems of determining optimal burn-in time and optimal replacement policy are considered.

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On bounds for some optimal policies in reliability

Journal of Applied Probability ◽

10.1239/jap/1034082122 ◽

2002 ◽

Vol 39 (3) ◽

pp. 491-502 ◽

Cited By ~ 4

Author(s):

Jie Mi

Keyword(s):

Lower Bound ◽

Residual Life ◽

Rate Function ◽

Replacement Policy ◽

Mean Residual Life ◽

Failure Rate Function ◽

Underlying Distribution ◽

Bathtub Shape ◽

Reliability Characteristics ◽

Quality Of Products

Often in the study of reliability and its applications, the goal is to maximize or minimize certain reliability characteristics or some cost functions. For example, burn-in is a procedure used to improve the quality of products before they are used in the field. A natural question which arises is how long the burn-in procedure should last in order to maximize the mean residual life or the conditional survival probability. In the literature, an upper bound for the optimal burn-in time is obtained by assuming that the underlying distribution of the products has a bathtub-shaped failure rate function; however, no lower bound is available. A similar question arises in studying replacement policy, warranty policy, and inspection models. This article gives a lower bound for the optimal burn-in time, and lower and upper bounds for the optimal replacement and warranty policies, under the same bathtub-shape assumption.

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