Inverted gamma as a life distribution

Lin, Cen-tsong; Duran, Benjamin S.; Lewis, T.

doi:10.1016/0026-2714(89)90352-1

Cited by 80 publications

(40 citation statements)

References 2 publications

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“…It has an inverted bathtub failure rate and it is an important competitive model for the Exponential distribution. It has been identified and discussed by Lin et al [9] as a lifetime model. If X is a non- [5], [8] are noticeable examples in the literature.…”

Section: Introductionmentioning

confidence: 99%

The Transmuted Inverse Exponential Distribution

Oguntunde¹,

Adejumo²

2014

IJASP

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This article introduces a two-parameter probability model which represents another generalization of the Inverse Exponential distribution by using the quadratic rank transmuted map. The proposed model is named Transmuted Inverse Exponential (TIE) distribution and its statistical properties are systematically studied. We provide explicit expressions for its moments, moment generating function, quantile function, reliability function and hazard function. We estimate the parameters of the TIE distribution using the method of maximum likelihood estimation (MLE). The hazard function of the model has an inverted bathtub shape and we propose the usefulness of the TIE distribution in modeling breast cancer and bladder cancer data sets.

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Section: Introductionmentioning

confidence: 99%

The Transmuted Inverse Exponential Distribution

Oguntunde¹,

Adejumo²

2014

IJASP

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“…If Y is an exponential random variable (rv), then X = 1 Y has an inverted exponential distribution. Lin et al (1989) and Dey (2007) discussed inverted exponential distribution (IED) to analyze lifetime data. Abouammoh and Alshingiti (2009) discussed generalized inverted exponential distribution (GIED) by introducing a shape parameter and discussed their statistical and reliability properties.…”

Section: Introductionmentioning

confidence: 99%

Inference on the Parameters and Reliability Characteristics of Generalized Inverted Scale Family of Distributions based on Records

Chaturvedi¹,

Malhotra²

2018

Stat., optim. inf. comput.

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A generalized inverted scale family of distributions is considered. Two measures of reliability are discussed, namely ρ(t) = P (X > t) and P = P (X > Y ). Point and interval estimation procedures are developed for the parameters, ρ(t) and P based on records. Two types of point estimators are developed -uniformly minimum variance unbiased estimators (UMVUES) and maximum likelihood estimators (MLES). A comparative study of different methods of estimation is done through simulation studies and asymptotic confidence intervals of the parameters based on MLE and log transformed MLE are constructed. Testing procedures are also developed for the parametric functions of the distribution and a real life example has been analysed for illustrative purposes.

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“…For example, in the course of the study of mortality associated with some of the diseases, the failure rate initially increases with time and reaches a peak after some finite period of times and then decline slowly see [9]. Thus, for analyse such type of data Inverted exponential distribution (IED) has been proposed as a lifetime model by [7]. [7], [8], [9] have advocated the use of IED as an appropriate model for non-monotonic satiation and also discussed the estimation procedure.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, for analyse such type of data Inverted exponential distribution (IED) has been proposed as a lifetime model by [7]. [7], [8], [9] have advocated the use of IED as an appropriate model for non-monotonic satiation and also discussed the estimation procedure. [8] has discussed the properties of the various estimators for the IED and also presented the estimation of the parameter, based on lower record values.…”

Section: Introductionmentioning

confidence: 99%

On the estimation of stress strength reliability parameter of inverted exponential distribution

Singh¹,

Singh²,

Yadav³

et al. 2015

IJSW

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This paper aims to estimate the stress-strength reliability parameter R = P (Y < X), when X and Y are independent inverted exponential random variable. We have also disscused some fundamental properties of the considered distribution. The maximum likelihood estimator (MLE) of R and its asymptotic distribution are obtained. The Bayesian estimation of the reliability parameter has been also discussed under the assumption of independent gamma prior. Numerical integration technique is used for Bayesian computation. The proposed estimators are compared in terms of their mean squared errors through the simulation study. Two real data sets representing survival of head and neck cancer patients are fitted using the inverted exponential distribution and used to estimate the stress-strength parameters and reliability.

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Inverted gamma as a life distribution

Cited by 80 publications

References 2 publications

The Transmuted Inverse Exponential Distribution

The Transmuted Inverse Exponential Distribution

Inference on the Parameters and Reliability Characteristics of Generalized Inverted Scale Family of Distributions based on Records

On the estimation of stress strength reliability parameter of inverted exponential distribution

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