scholarly journals ON BIVARIATE EXPONENTIATED EXTENDED WEIBULL FAMILY OF DISTRIBUTIONS

2016 ◽  
Vol 38 (2) ◽  
pp. 564 ◽  
Author(s):  
Rasool Roozegar ◽  
Ali Akbar Jafari
Keyword(s):  
Power Series ◽  
Residual Life ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Rate Function ◽  
Mean Residual Life ◽  
New Class ◽  
Special Cases ◽  
Exponentiated Weibull ◽  
Exponential Power

In this paper, we introduce a new class of distributions by compounding the exponentiated extended Weibull family and power series family. This distribution contains several lifetime models such as the complementary extended Weibull-power series, generalized exponential-power series, generalized linear failure rate-power series, exponentiated Weibull-power series, generalized modifiedWeibull-power series, generalized Gompertz-power series and exponentiated extendedWeibull distributions as special cases. We obtain several properties of this new class of distributions such as Shannon entropy, mean residual life, hazard rate function, quantiles and moments. The maximum likelihood estimation procedure via a EM-algorithm is presented.

scholarly journals A GENERALIZATION OF SUJATHA DISTRIBUTION AND ITS APPLICATIONS WITH REAL LIFETIME DATA

2017 ◽  
Vol 22 (1) ◽  
pp. 66-83 ◽  
Author(s):  
Rama Shanker ◽  
Kamlesh Kumar Shukla ◽  
Hagos Fesshaye
Keyword(s):  
Residual Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Stochastic Ordering ◽  
Rate Function ◽  
Mean Residual Life ◽  
Exponential Distributions ◽  
Lorenz Curves ◽  
Two Parameter ◽  
Life Function

A two-parameter generalization of Sujatha distribution (AGSD), which includes Lindley distribution and Sujatha distribution as particular cases, has been proposed. It's important mathematical and statistical properties including its shape for varying values of parameters, moments, coefficient of variation, skewness, kurtosis, index of dispersion, hazard rate function, mean residual life function, stochastic ordering, mean deviations, Bonferroni and Lorenz curves, and stress-strength reliability have been discussed. Maximum likelihood estimation method has been discussed for estimating its parameters. AGSD provides better fit than Sujatha, Aradhana, Lindley and exponential distributions for modeling real lifetime data.Journal of Institute of Science and TechnologyVolume 22, Issue 1, July 2017, Page: 66-83

scholarly journals Properties and inference for a new class of XGamma distributions with an application

2019 ◽  
Vol 13 (4) ◽  
pp. 335-346
Author(s):  
Hayrinisa Demirci Biçer
Keyword(s):  
Monte Carlo ◽  
Hazard Rate ◽  
Residual Life ◽  
Moment Generating Function ◽  
Distribution Model ◽  
Mean Residual Life ◽  
Survival Functions ◽  
Data Set ◽  
New Class ◽  
Special Cases

Abstract The current paper introduces a new flexible probability distribution model called transmuted XGamma distribution which pullulates from the XGamma distribution and possesses the characteristics of XGamma distribution in special cases. In the paper, we obtain the explicit expressions for some important statistical properties of the introduced distribution such as hazard rate and survival functions, mean residual life, moment-generating function, moments, skewness, kurtosis, distribution of its order statistics, Lorenz and Bonferroni curves. Besides obtaining the various effective estimators for the parameters of the distribution, estimation performances of these estimators are comparatively examined with a series of Monte Carlo simulations. Furthermore, to demonstrate the modeling ability of the proposed distribution on real-world phenomena, an illustrative example is performed by using an actual data set in connection with the field of the lifetime.

ON THE RELIABILITY PROPERTIES OF SOME WEIGHTED MODELS OF BATHTUB SHAPED HAZARD RATE DISTRIBUTIONS

2012 ◽  
Vol 27 (1) ◽  
pp. 125-140 ◽  
Author(s):  
M. Shafaei Noughabi ◽  
G.R. Mohtashami Borzadaran ◽  
A.H. Rezaei Roknabadi
Keyword(s):  
Order Statistics ◽  
Hazard Rate ◽  
Residual Life ◽  
Rate Function ◽  
Mean Residual Life ◽  
Special Cases ◽  
Weighted Model ◽  
The Times ◽  
The One ◽  
Useful Lifetime

Let F be a bathtub-shaped (BT) hazard rate distribution function. It has been shown that the hazard rate function of the order statistics may be BT, increasing, etc. Then, we have carried out a graphical study for some useful lifetime models.Moreover, we are interested to compare the time that maximizes the mean residual life (MRL) function of F with the one related to a general weighted model in terms of their locations. Also, the times maximizing the conditional reliability proposed by Mi [13] of F have been compared with the corresponding times of a general weighted model. As special cases, we consider order statistics and the proportional hazard rate model.

scholarly journals A Distribution for Instantaneous Failures

Stats ◽  
2019 ◽  
Vol 2 (2) ◽  
pp. 247-258 ◽  
Author(s):  
Pedro L. Ramos ◽  
Francisco Louzada
Keyword(s):  
Residual Life ◽  
Likelihood Estimation ◽  
Estimation Methods ◽  
Mean Residual Life ◽  
Parameter Distribution ◽  
Coverage Probabilities ◽  
Instantaneous Failures ◽  
The Relationship ◽  
Mean Variance ◽  
New Distribution

A new one-parameter distribution is proposed in this paper. The new distribution allows for the occurrence of instantaneous failures (inliers) that are natural in many areas. Closed-form expressions are obtained for the moments, mean, variance, a coefficient of variation, skewness, kurtosis, and mean residual life. The relationship between the new distribution with the exponential and Lindley distributions is presented. The new distribution can be viewed as a combination of a reparametrized version of the Zakerzadeh and Dolati distribution with a particular case of the gamma model and the occurrence of zero value. The parameter estimation is discussed under the method of moments and the maximum likelihood estimation. A simulation study is performed to verify the efficiency of both estimation methods by computing the bias, mean squared errors, and coverage probabilities. The superiority of the proposed distribution and some of its concurrent distributions are tested by analyzing four real lifetime datasets.

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.

A New Class of Beta-Complementary Exponential Power Series Distributions

2018 ◽  
Vol 46 (5) ◽  
pp. 20170036
Author(s):  
E. Mahmoudi ◽  
R. S. Meshkat ◽  
M. Entezari
Keyword(s):  
Power Series ◽  
New Class ◽  
Exponential Power ◽  
Power Series Distributions

ON A CLASS OF GENERALIZED MARSHALL–OLKIN BIVARIATE DISTRIBUTIONS AND SOME RELIABILITY CHARACTERISTICS

2013 ◽  
Vol 27 (2) ◽  
pp. 261-275 ◽  
Author(s):  
Ramesh C. Gupta ◽  
S.N.U.A. Kirmani ◽  
N. Balakrishnan
Keyword(s):  
Residual Life ◽  
Bivariate Distribution ◽  
Point Of View ◽  
Mean Residual Life ◽  
Bivariate Distributions ◽  
Bivariate Exponential Distribution ◽  
Bivariate Model ◽  
Reliability Characteristics ◽  
Bivariate Exponential ◽  
Special Cases

We consider here a general class of bivariate distributions from reliability point of view, and refer to it as generalized Marshall–Olkin bivariate distributions. This class includes as special cases the Marshall–Olkin bivariate exponential distribution and the class of bivariate distributions studied recently by Sarhan and Balakrishnan [25]. For this class, the reliability, survival, hazard, and mean residual life functions are all derived, and their monotonicity is discussed for the marginal as well as the conditional distributions. These functions are also studied for the series and parallel systems based on this bivariate distribution. Finally, the Clayton association measure for this bivariate model is derived in terms of the hazard gradient.

scholarly journals Fisher consistent estimation of regression parameter in the proportional mean residual life model with frailty

Ekonomia ◽  
2021 ◽  
Vol 27 (2) ◽  
pp. 81-88
Author(s):  
Magdalena Skolimowska-Kulig
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Regression Models ◽  
Residual Life ◽  
Likelihood Estimation ◽  
Mean Residual Life ◽  
Regression Parameter ◽  
Consistent Estimation ◽  
Regression Parameters ◽  
Life Model

In the article, we consider the Fisher consistent estimation of the regression parameters in the proportional mean residual life model with arbitrary frailty. It is discussed that conventional estimation procedures, such as the maximum likelihood estimation or Cox’s approach, which are employed in common regression models, may also yield consistent inference in the extended models.

On bounds for some optimal policies in reliability

2002 ◽  
Vol 39 (3) ◽  
pp. 491-502 ◽  
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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