Further Results Involving the Mit Order and the Imit Class

Ahmad, Ibrahim A.; Kayid, Mohamed; Pellerey, Franco

doi:10.1017/s0269964805050229

Cited by 71 publications

(40 citation statements)

References 22 publications

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“…When H 0 is rejected, and thus F is DRHR, estimating F as well as other related functions, such as the mean inactivity time (MIT), is an interesting and open problem. Also, it would be interesting to study a similar approach to the increasing mean inactivity time (IMIT) class [19][20][21], and other related classes.…”

Section: Resultsmentioning

confidence: 99%

Testing behavior of the reversed hazard rate

Kayid¹,

Al-nahawati²,

Ahmad³

2011

Applied Mathematical Modelling

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a b s t r a c tThe concept of reversed hazard rate of a random life is defined as the ratio between the life probability density to its distribution function. This concept plays a role in analyzing censored data and is applicable in such areas as Forensic Sciences. In this investigation, we address the question of testing the reversed hazard rate where the null is that the reversed hazard rate is an assigned function while the alternative is that it is decreasing but not equal to the null function. Two approaches are discussed: one is based on the empirical distribution function while the other is based on the celebrated kernel methods. The limiting distributions of the test statistics are given and its asymptotic Pittman efficiencies are evaluated for well-known alternatives when the null distribution is exponential. Some other related problems are also addressed.

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Section: Resultsmentioning

confidence: 99%

Testing behavior of the reversed hazard rate

Kayid¹,

Al-nahawati²,

Ahmad³

2011

Applied Mathematical Modelling

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“…In particular, if r = 1, thenm 1 (t) represents a function called the mean idle time or inactivity time (MIT) or reversed residual life (MRRL) function that indicates the expected inactive life length for a unit which is first observed down at age t. The properties of MIT function have been explored by Ahmad et al (2005) and Kayid and Ahmad (2004).…”

Section: Definition 471 Let X Be a Random Variable Denoting The Lifmentioning

confidence: 99%

The Generalized Additive Weibull-G Family of Distributions

Hassan¹,

Hemeda²,

Maiti³

et al. 2017

IJSP

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In this paper, we present a new family, depending on additive Weibull random variable as a generator, called the generalized additive Weibull generated-family (GAW-G) of distributions with two extra parameters. The proposed family involves several of the most famous classical distributions as well as the new generalized Weibull-G family which already accomplished by Cordeiro et al. (2015). Four special models are displayed. The expressions for the incomplete and ordinary moments, quantile, order statistics, mean deviations, Lorenz and Benferroni curves are derived. Maximum likelihood method of estimation is employed to obtain the parameter estimates of the family. The simulation study of the new models is conducted. The efficiency and importance of the new generated family is examined through real data sets.

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“…The MRRL of X can be obtained by setting n = 1 in the above equation. The properties of the mean inactivity time have been considered by many authors, see e.g., Kayid and Ahmad (2004) and Ahmad et al (2005).…”

Section: Reversed Residual Life Functionmentioning

confidence: 99%

The Transmuted Marshall-Olkin Fr\'{e}chet Distribution: Properties and Applications

Afify¹,

Hamedani²,

Ghosh³

et al. 2015

IJSP

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This paper introduces a new four-parameter lifetime model, which extends the Marshall-Olkin Fréchet distribution introduced by Krishna et al. (2013), called the transmuted Marshall-Olkin Fréchet distribution. Various structural properties including ordinary and incomplete moments, quantile and generating function, Rényi and q-entropies and order statistics are derived. The maximum likelihood method is used to estimate the model parameters. We illustrate the superiority of the proposed distribution over other existing distributions in the literature in modeling two real life data sets.

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Further Results Involving the Mit Order and the Imit Class

Cited by 71 publications

References 22 publications

Testing behavior of the reversed hazard rate

Testing behavior of the reversed hazard rate

The Generalized Additive Weibull-G Family of Distributions

The Transmuted Marshall-Olkin Fr\'{e}chet Distribution: Properties and Applications

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