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 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 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 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 The beta Gumbel distribution

2004 ◽  
Vol 2004 (4) ◽  
pp. 323-332 ◽  
Author(s):  
Saralees Nadarajah ◽  
Samuel Kotz
Keyword(s):  
Hazard Rate ◽  
Gumbel Distribution ◽  
Random Variable ◽  
Rate Function ◽  
Comprehensive Treatment ◽  
Hazard Rate Function ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
New Distribution ◽  
Skewness And Kurtosis

The Gumbel distribution is perhaps the most widely applied statistical distribution for problems in engineering. In this paper, we introduce a generalization—referred to as the beta Gumbel distribution—generated from the logit of a beta random variable. We provide a comprehensive treatment of the mathematical properties of this new distribution. We derive the analytical shapes of the corresponding probability density function and the hazard rate function and provide graphical illustrations. We calculate expressions for thenth moment and the asymptotic distribution of the extreme order statistics. We investigate the variation of the skewness and kurtosis measures. We also discuss estimation by the method of maximum likelihood. We hope that this generalization will attract wider applicability in engineering.

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.

scholarly journals Modeling Extreme Values Utilizing an Asymmetric Probability Function

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1730
Author(s):  
Mohammed M. A. Almazah ◽  
Muqrin A. Almuqrin ◽  
Mohamed. S. Eliwa ◽  
Mahmoud El-Morshedy ◽  
Haitham M. Yousof
Keyword(s):  
Hazard Rate ◽  
Extreme Values ◽  
Residual Life ◽  
Real Data ◽  
Moment Generating Function ◽  
Rate Function ◽  
Estimation Methods ◽  
Model Parameters ◽  
Hazard Rate Function ◽  
Data Application

In this article, a new flexible probability density function with three parameters is proposed for modeling asymmetric data (positive and negative) with different types of kurtosis (mesokurtic, leptokurtic and platykurtic). Some of its statistical and reliability properties, including hazard rate function, moments, moment generating function, incomplete moments, mean deviations, moment of the residual life, moment of the reversed residual life, and order statistics are derived. Its hazard rate function can be either constant, increasing-constant, decreasing-constant, U shape, upside down shape or upside down-U shape. Seven classical estimation methods are considered to estimate the unknown model parameters. Monte Carlo simulation experiments are performed to compare the performance of the seven different estimation methods. Finally, a distinctive asymmetric real data application is analyzed for illustrating the flexibility of the new model.

scholarly journals Kumaraswamy Generalized Power Lomax Distributionand Its Applications

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 28-45
Author(s):  
Vasili B.V. Nagarjuna ◽  
R. Vishnu Vardhan ◽  
Christophe Chesneau
Keyword(s):  
Hazard Rate ◽  
Real Data ◽  
Rate Function ◽  
Maximum Likelihood Estimates ◽  
Parameter Estimates ◽  
Parameter Distribution ◽  
Data Sets ◽  
Lomax Distribution ◽  
Entropy Measures ◽  
Modeling Behavior

In this paper, a new five-parameter distribution is proposed using the functionalities of the Kumaraswamy generalized family of distributions and the features of the power Lomax distribution. It is named as Kumaraswamy generalized power Lomax distribution. In a first approach, we derive its main probability and reliability functions, with a visualization of its modeling behavior by considering different parameter combinations. As prime quality, the corresponding hazard rate function is very flexible; it possesses decreasing, increasing and inverted (upside-down) bathtub shapes. Also, decreasing-increasing-decreasing shapes are nicely observed. Some important characteristics of the Kumaraswamy generalized power Lomax distribution are derived, including moments, entropy measures and order statistics. The second approach is statistical. The maximum likelihood estimates of the parameters are described and a brief simulation study shows their effectiveness. Two real data sets are taken to show how the proposed distribution can be applied concretely; parameter estimates are obtained and fitting comparisons are performed with other well-established Lomax based distributions. The Kumaraswamy generalized power Lomax distribution turns out to be best by capturing fine details in the structure of the data considered.

Reliability Concepts

2018 ◽  
pp. 1-22
Keyword(s):  
Hazard Rate ◽  
Failure Process ◽  
Reliability Function ◽  
Rate Function ◽  
Cumulative Distribution ◽  
Hazard Rate Function ◽  
Reliability Engineering ◽  
Probability Models ◽  
Engineering Design Process ◽  
Basic Concepts

The first chapter introduces basic concepts of Reliability and their relationships. Four probability functions—reliability function, cumulative distribution function, probability density function, and hazard rate function—that completely characterize the failure process are defined. Three failure rates—MTBF, MTTF, MTTR—that play important role in reliability engineering design process are explained here. The three patterns of failures, DFR, CFR, and IFR, are discussed with reference to the bathtub curve. Two probability models, Exponential and Weibull, are presented. Series and parallel systems and application areas of reliability are also presented.

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