The Inverse Gaussian Distribution as a Lifetime Model

Chhikara, Raj S.; Folks, J. Leroy

doi:10.1080/00401706.1977.10489586

Cited by 253 publications

(85 citation statements)

References 6 publications

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“…where '*' is the convolution operator defined by 474 M. Aslam Chaudhry [6] We can write (20) in the operational form (see [9, page 131(20) From (18)- (22) The following corollary is the consequence of (16) and does not seem to be known in the literature.…”

Section: (Lnt)\^-^-\exp(-at-brmentioning

confidence: 99%

“…Some of the probabilistic properties of the distribution (2) were investigated in [4], [6], [10], [14], [19], [20]. Sichel [17] used (2) to construct mixtures of Poisson distributions and Barndorff-Nielson [4] used it to obtain the generalized hyperbolic distribution as a mixture of normal distributions.…”

Section: Exp(-ar -Br X )Dt = 2(b/a) A/2 K a (2vab) Jomentioning

confidence: 99%

“…The model (1) has been used in the statistical theory of demographic rates and in reliability theory, (see [6], [7], [13], [14], [16], [17], [19], [20]). Good [10] proposed the generalized inverse Guassian distribution …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On a family of logarithmic and exponential integrals occurring in probability and reliability theory

Chaudhry

1994

J. Aust. Math. Soc. Series B, Appl. Math

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Section: (Lnt)\^-^-\exp(-at-brmentioning

confidence: 99%

Section: Exp(-ar -Br X )Dt = 2(b/a) A/2 K a (2vab) Jomentioning

confidence: 99%

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On a family of logarithmic and exponential integrals occurring in probability and reliability theory

Chaudhry

1994

J. Aust. Math. Soc. Series B, Appl. Math

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“…The data set was originally reported by Von Alven (1964) and later Chhikara and Folks (1977) used it on the inverse Gaussian distribution. The results of the fits are listed in Table 4.…”

Section: Applicationmentioning

confidence: 99%

The Adjusted Log-logistic Generalized Exponential Distribution with Application to Lifetime Data

Okorie¹,

Akpanta²,

Ohakwe³

et al. 2017

IJSP

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This paper introduces a new generator of probability distribution-the adjusted log-logistic generalized (ALLoG) distribution and a new extension of the standard one parameter exponential distribution called the adjusted log-logistic generalized exponential (ALLoGExp) distribution. The ALLoGExp distribution is a special case of the ALLoG distribution and we have provided some of its statistical and reliability properties. Notably, the failure rate could be monotonically decreasing, increasing or upside-down bathtub shaped depending on the value of the parameters δ and θ. The method of maximum likelihood estimation was proposed to estimate the model parameters. The importance and flexibility of the ALLoGExp distribution was demonstrated with a real and uncensored lifetime data set and its fit was compared with five other exponential related distributions. The results obtained from the model fittings shows that the ALLoGExp distribution provides a reasonably better fit than the one based on the other fitted distributions. The ALLoGExp distribution is therefore recommended for effective modelling of lifetime data sets.

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“…From a reliability point of view, Chhikara and Folks (1977) showed that if the lifetime of a machine has the inverse Gaussian distribution and the shape parameter is less than 2 and given that the machine has survived up to time t 0 (a known value), then the mean residual time will eventually exceed the original mean lifetime. In practice, the shape parameter is typically unknown.…”

Section: Introductionmentioning

confidence: 99%

Likelihood Based Inference for the Shape Parameter of the Inverse Gaussian Distribution

Lee¹,

Kang²,

Kim³

2008

Communications for Statistical Applications and Methods

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Small sample likelihood based inference for the shape parameter of the inverse Gaussian distribution is the purpose of this paper. When shape parameter is of interest, the signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic are derived. Hsieh (1990) gave a statistical inference for the shape parameter based on an exact method. Throughout simulation, we will compare the statistical properties of the proposed statistics to the statistic given by Hsieh (1990) in term of confidence interval and power of test. We also discuss a real data example.

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The Inverse Gaussian Distribution as a Lifetime Model

Cited by 253 publications

References 6 publications

On a family of logarithmic and exponential integrals occurring in probability and reliability theory

On a family of logarithmic and exponential integrals occurring in probability and reliability theory

The Adjusted Log-logistic Generalized Exponential Distribution with Application to Lifetime Data

Likelihood Based Inference for the Shape Parameter of the Inverse Gaussian Distribution

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