scholarly journals Weibull Model Allowing Nearly Instantaneous Failures

2007 ◽  
Vol 2007 ◽  
pp. 1-11 ◽  
Author(s):  
C. D. Lai ◽  
Michael B. C. Khoo ◽  
K. Muralidharan ◽  
M. Xie
Keyword(s):  
Probability Density Function ◽  
Hazard Rate ◽  
Survival Function ◽  
Weibull Model ◽  
Rate Function ◽  
Model Parameters ◽  
Hazard Rate Function ◽  
Modified Model ◽  
Instantaneous Failures ◽  
Early Failures

A generalized Weibull model that allows instantaneous or early failures is modified so that the model can be expressed as a mixture of the uniform distribution and the Weibull distribution. Properties of the resulting distribution are derived; in particular, the probability density function, survival function, and the hazard rate function are obtained. Some selected plots of these functions are also presented. An R script was written to fit the model parameters. An application of the modified model is illustrated.

scholarly journals A New Flexible Bathtub-Shaped Modification of the Weibull Model: Properties and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Qinghu Liao ◽  
Zubair Ahmad ◽  
Eisa Mahmoudi ◽  
G. G. Hamedani
Keyword(s):  
Weibull Distribution ◽  
Hazard Rate ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Weibull Model ◽  
Rate Function ◽  
Model Parameters ◽  
Hazard Functions ◽  
Practical Applications ◽  
Nonnested Models

Many studies have suggested the modifications and generalizations of the Weibull distribution to model the nonmonotone hazards. In this paper, we combine the logarithms of two cumulative hazard rate functions and propose a new modified form of the Weibull distribution. The newly proposed distribution may be called a new flexible extended Weibull distribution. Corresponding hazard rate function of the proposed distribution shows flexible (monotone and nonmonotone) shapes. Three different characterizations along with some mathematical properties are provided. We also consider the maximum likelihood estimation procedure to estimate the model parameters. For the illustrative purposes, two real applications from reliability engineering with bathtub-shaped hazard functions are analyzed. The practical applications show that the proposed model provides better fits than the other nonnested models.

scholarly journals Slashed Lomax Distribution and Regression Model

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1877
Author(s):  
Huihui Li ◽  
Weizhong Tian
Keyword(s):  
Regression Model ◽  
Hazard Rate ◽  
Rate Function ◽  
Model Parameters ◽  
Asymmetric Distribution ◽  
Hazard Rate Function ◽  
Simulation Studies ◽  
Ecm Algorithm ◽  
Lomax Distribution ◽  
Skewness And Kurtosis

In this article, the slashed Lomax distribution is introduced, which is an asymmetric distribution and can be used for fitting thick-tailed datasets. Various properties are explored, such as the density function, hazard rate function, Renyi entropy, r-th moments, and the coefficients of the skewness and kurtosis. Some useful characterizations of this distribution are obtained. Furthermore, we study a slashed Lomax regression model and the expectation conditional maximization (ECM) algorithm to estimate the model parameters. Simulation studies are conducted to evaluate the performances of the proposed method. Finally, two sets of data are applied to verify the importance of the slashed Lomax distribution.

scholarly journals The Inverse Sushila Distribution: Properties and Application

2020 ◽  
pp. 28-39
Author(s):  
A. A. Adetunji ◽  
J. A. Ademuyiwa ◽  
O. A. Adejumo
Keyword(s):  
Hazard Rate ◽  
Survival Function ◽  
Likelihood Estimation ◽  
Stochastic Ordering ◽  
Rate Function ◽  
Lifetime Data ◽  
Hazard Rate Function ◽  
Cumulative Hazard ◽  
Fundamental Properties ◽  
Proposed Model

In this paper, a new lifetime distribution called the Inverse Sushila Distribution (ISD) is proposed. Its fundamental properties like the density function, distribution function, hazard rate function, survival function, cumulative hazard rate function, order statistics, moments, moments generating function, maximum likelihood estimation, quantiles function, Rényi entropy and stochastic ordering are obtained. The distribution offers more flexibility in modelling upside-down bathtub lifetime data. The proposed model is applied to a lifetime data and its performance is compared with some other related distributions.

scholarly journals Analysis of Type-II Censored Competing Risks’ Data under Reduced New Modified Weibull Distribution

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Saad J. Almalki ◽  
Tahani A. Abushal ◽  
M. D. Alsulami ◽  
G. A. Abd-Elmougod
Keyword(s):  
Competing Risks ◽  
Hazard Rate ◽  
Rate Function ◽  
Likelihood Method ◽  
Mcmc Methods ◽  
Model Parameters ◽  
Type Ii ◽  
Hazard Rate Function ◽  
Monte Carlo Simulation Study ◽  
Modified Weibull

Models with the bathtub-shaped hazard rate function are widely used in lifetime analysis and reliability engineering. In this paper, we adopted the reduced new modified Weibull (RNMW) distribution with a bathtub-shaped hazard rate function. Under consideration that the population units are failing with two independent causes of failure and the failure time is distributed with RNMW distribution, we formulate the model which is known as competing risks model. The model parameters under the type-II censoring scheme are estimated with the maximum likelihood method with the corresponding asymptotic confidence intervals. Also, the Bayes point and credible intervals with the help of MCMC methods are constructed. The real and simulated datasets are analyzed for illustrative purposes. Finally, the estimators are compared with the Monte Carlo simulation study.

scholarly journals A Mathematical WGED – Model Approach on Short-Term High in Density Exercise Training, Attenuated Acute Exercise – Induced Growth Hormone Response

2019 ◽  
Vol 8 (1) ◽  
pp. 1-5
Author(s):  
M. Kaliraja ◽  
K. Perarasan
Keyword(s):  
Growth Hormone ◽  
Exponential Distribution ◽  
Hazard Rate ◽  
Acute Exercise ◽  
Survival Function ◽  
Life Time ◽  
Rate Function ◽  
Hazard Rate Function ◽  
Short Term ◽  
Exercise Induced

In the current manuscript, we have demonstrated the recent generalization of Weibull-G exponential distribution (three-parameter) and it is a very familiar distribution as compared to other distribution.It has been found that Weibull-G exponential distribution (WGED) can be utilized pretty efficiently to evaluate the biological data in the position of gamma and log-normal Weibull distributions. It has two shape parameters and the three scale parameters namely, a, b, λ. Some of its statistical properties are acquired, which includes reserved hazard function, probability-density function, hazard-rate function and survival function. Our aim is to shore-up the results of life-time using three-parameter Weibull generalized exponential distribution. Hence, the corresponding probability functions, hazard-rate function, survival function as well as reserved hazard-rate function has been analyzed in the 3 weeks of high-intensity exercise training in short-term. The outcomes of the present study supporting the results of life-time data that the interim elevated intensity exercise activity attenuated an acute exercise induced growth hormone release.

scholarly journals The Topp-Leone odd log-logistic Gumbel Distribution: Properties and Applications

2020 ◽  
Vol 9 (2) ◽  
pp. 288-310
Author(s):  
Fazlollah Lak ◽  
Morad Alizadeh ◽  
Hamid Karamikabir
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Hazard Rate ◽  
Gumbel Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Rate Function ◽  
Model Parameters ◽  
Data Sets ◽  
Hazard Rate Function

In this article, the Topp-Leone odd log-logistic Gumbel (TLOLL-Gumbel) family of distribution have beenstudied. This family, contains the very flexible skewed density function. We study many aspects of the new model like hazard rate function, asymptotics, useful expansions, moments, generating Function, R´enyi entropy and order statistics. We discuss maximum likelihood estimation of the model parameters. Further, we study flexibility of the proposed family are illustrated of two real data sets.

scholarly journals Exponentiated Frechet Distribution with Application in Temperature of Assam, India Overview with New Properties and Estimation

2021 ◽  
pp. 211-225
Author(s):  
Umme Habibah Rahman ◽  
Tanusree Deb Roy
Keyword(s):  
Hazard Rate ◽  
Goodness Of Fit ◽  
Survival Function ◽  
Information Matrix ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Rate Function ◽  
Hazard Rate Function ◽  
Fréchet Distribution ◽  
Frechet Distribution

In this paper, a new kind of distribution has suggested with the concept of exponentiate. The reliability analysis including survival function, hazard rate function, reverse hazard rate function and mills ratio has been studied here. Its quantile function and order statistics are also included. Parameters of the distribution are estimated by the method of Maximum Likelihood estimation method along with Fisher information matrix and confidence intervals have also been given. The application has been discussed with the 30 years temperature data of Silchar city, Assam, India. The goodness of fit of the proposed distribution has been compared with Frechet distribution and as a result, for all 12 months, the proposed distribution fits better than the Frechet distribution.

scholarly journals PCM Transformation: Properties and Their Estimation

2021 ◽  
Author(s):  
Dinesh Kumar ◽  
Pawan Kumar ◽  
Pradip Kumar ◽  
Sanjay Kumar Singh ◽  
Umesh Singh
Keyword(s):  
Hazard Rate ◽  
Survival Function ◽  
Stochastic Ordering ◽  
Information Criterion ◽  
Moment Generating Function ◽  
Rate Function ◽  
Hazard Rate Function ◽  
Test Statistic ◽  
Bayesian Approaches

In the present piece of work, we are going to propose a new trigonometry based transformation called PCM transformation. We have been obtained its various statistical properties such as survival function, hazard rate function, reverse-hazard rate function, moment generating function, median, stochastic ordering etc. Maximum Likelihood Estimator (MLE) method under classical approach and Bayesian approaches are tackled to obtain the estimate of unknown parameter. A real dataset has been applied to check its fitness on the basis of fitting criterions Akaike Information criterion (AIC), Bayesian Information criterion (BIC), log-likelihood (-LL) and Kolmogrov-Smirnov (KS) test statistic values in real sense. A simulation study is also being conducted to assess the estimator’s long-term attitude and compared over some chosen distributions.

scholarly journals A Flexible Extension to an Extreme Distribution

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 745
Author(s):  
Mohamed S. Eliwa ◽  
Fahad Sameer Alshammari ◽  
Khadijah M. Abualnaja ◽  
Mahmoud El-Morshedy
Keyword(s):  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Rate Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Hazard Rate Function ◽  
Censored Samples ◽  
Extreme Distribution ◽  
Extreme Model

The aim of this paper is not only to propose a new extreme distribution, but also to show that the new extreme model can be used as an alternative to well-known distributions in the literature to model various kinds of datasets in different fields. Several of its statistical properties are explored. It is found that the new extreme model can be utilized for modeling both asymmetric and symmetric datasets, which suffer from over- and under-dispersed phenomena. Moreover, the hazard rate function can be constant, increasing, increasing–constant, or unimodal shaped. The maximum likelihood method is used to estimate the model parameters based on complete and censored samples. Finally, a significant amount of simulations was conducted along with real data applications to illustrate the use of the new extreme distribution.

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