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 Sharp bounds for exponential approximations under a hazard rate upper bound

2015 ◽  
Vol 52 (03) ◽  
pp. 841-850 ◽  
Author(s):  
Mark Brown
Keyword(s):  
Exponential Distribution ◽  
Hazard Rate ◽  
Residual Life ◽  
Continuous Distribution ◽  
Rate Function ◽  
Mean Residual Life ◽  
Birth And Death Processes ◽  
Absolutely Continuous ◽  
Sharp Bounds ◽  
Life Distributions

Consider an absolutely continuous distribution on [0, ∞) with finite meanμand hazard rate functionh(t) ≤bfor allt. Forbμclose to 1, we would expectFto be approximately exponential. In this paper we obtain sharp bounds for the Kolmogorov distance betweenFand an exponential distribution with meanμ, as well as betweenFand an exponential distribution with failure rateb. We apply these bounds to several examples. Applications are presented to geometric convolutions, birth and death processes, first-passage times, and to decreasing mean residual life distributions.

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.

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 Sharp bounds for exponential approximations under a hazard rate upper bound

2015 ◽  
Vol 52 (3) ◽  
pp. 841-850 ◽  
Author(s):  
Mark Brown
Keyword(s):  
Exponential Distribution ◽  
Hazard Rate ◽  
Residual Life ◽  
Continuous Distribution ◽  
Rate Function ◽  
Mean Residual Life ◽  
Birth And Death Processes ◽  
Absolutely Continuous ◽  
Sharp Bounds ◽  
Life Distributions

Consider an absolutely continuous distribution on [0, ∞) with finite mean μ and hazard rate function h(t) ≤ b for all t. For bμ close to 1, we would expect F to be approximately exponential. In this paper we obtain sharp bounds for the Kolmogorov distance between F and an exponential distribution with mean μ, as well as between F and an exponential distribution with failure rate b. We apply these bounds to several examples. Applications are presented to geometric convolutions, birth and death processes, first-passage times, and to decreasing mean residual life distributions.

Dynamic multivariate mean residual life functions

1991 ◽  
Vol 28 (03) ◽  
pp. 613-629 ◽  
Author(s):  
Moshe Shaked ◽  
J. George Shanthikumar
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Stochastic Ordering ◽  
Partial Ordering ◽  
Mean Residual Life ◽  
Positive Dependence ◽  
Basic Properties ◽  
Rate Functions ◽  
Hazard Rate Ordering ◽  
Weak Notion

In this paper we introduce and study a dynamic notion of mean residual life (mrl) functions in the context of multivariate reliability theory. Basic properties of these functions are derived and their relationship to the multivariate conditional hazard rate functions is studied. A partial ordering, called the mrl ordering, of non-negative random vectors is introduced and its basic properties are presented. Its relationship to stochastic ordering and to other related orderings (such as hazard rate ordering) is pointed out. Using this ordering it is possible to introduce a weak notion of positive dependence of random lifetimes. Some properties of this positive dependence notion are given. Finally, using the mrl ordering, a dynamic notion of multivariate DMRL (decreasing mean residual life) is introduced and studied. The relationship of this multivariate DMRL notion to other notions of dynamic multivariate aging is highlighted in this paper.

PRESERVATION OF STOCHASTIC ORDERS UNDER MIXTURES OF EXPONENTIAL DISTRIBUTIONS

2006 ◽  
Vol 20 (4) ◽  
pp. 655-666 ◽  
Author(s):  
Jarosław Bartoszewicz ◽  
Magdalena Skolimowska
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Stochastic Order ◽  
Stochastic Orders ◽  
Mean Residual Life ◽  
Exponential Distributions ◽  
Dispersive Order ◽  
Mixing Distributions ◽  
Convex Transform Order ◽  
Star Order

Recently, Bartoszewicz [5,6] considered mixtures of exponential distributions treated as the Laplace transforms of mixing distributions and established some stochastic order relations between them: star order, dispersive order, dilation. In this article the preservation of the likelihood ratio, hazard rate, reversed hazard rate, mean residual life, and excess wealth orders under exponential mixtures is studied. Some new preservation results for the dispersive order are given, as well as the preservation of the convex transform order, and the star one is discussed.

MEAN RESIDUAL LIFE FUNCTION FOR ADDITIVE AND MULTIPLICATIVE HAZARD RATE MODELS

2015 ◽  
Vol 30 (2) ◽  
pp. 281-297 ◽  
Author(s):  
Ramesh C. Gupta
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Turning Points ◽  
Sufficient Conditions ◽  
Mean Residual Life ◽  
Residual Life Function ◽  
Mean Residual Life Function ◽  
Hazard Rate Models ◽  
The Mean ◽  
Life Function

This paper deals with the mean residual life function (MRLF) and its monotonicity in the case of additive and multiplicative hazard rate models. It is shown that additive (multiplicative) hazard rate does not imply reduced (proportional) MRLF and vice versa. Necessary and sufficient conditions are obtained for the two models to hold simultaneously. In the case of non-monotonic failure rates, the location of the turning points of the MRLF is investigated in both the cases. The case of random additive and multiplicative hazard rate is also studied. The monotonicity of the mean residual life is studied along with the location of the turning points. Examples are provided to illustrate the results.

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