Inferences on the difference and ratio of the means of two inverse Gaussian distributions

Krishnamoorthy, K.; Tian, Lili

doi:10.1016/j.jspi.2007.09.005

Cited by 24 publications

(10 citation statements)

References 17 publications

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“…Appendices A and B respectively provide GPQs for the log-location-scale distribution families and the gamma distribution. GPQs for IG distribution could be found in Krishnamoorthy and Tian (2008).…”

Section: Discrimination Between Lifetime Modelsmentioning

confidence: 99%

Pairwise model discrimination with applications in lifetime distributions and degradation processes

Chen

Xiao

2019

Naval Research Logistics

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Reliability data obtained from life tests and degradation tests have been extensively used for purposes such as estimating product reliability and predicting warranty costs. When there is more than one candidate model, an important task is to discriminate between the models. In the literature, the model discrimination was often treated as a hypothesis test and a pairwise model discrimination procedure was carried out. Because the null distribution of the test statistic is unavailable in most cases, the large sample approximation and the bootstrap were frequently used to find the acceptance region of the test. Although these two methods are asymptotically accurate, their performance in terms of size and power is not satisfactory in small sample size. To enhance the small‐sample performance, we propose a new method to approximate the null distribution, which builds on the idea of generalized pivots. Conventionally, the generalized pivots were often used for interval estimation of a certain parameter or function of parameters in presence of nuisance parameters. In this study, we further extend the idea of generalized pivots to find the acceptance region of the model discrimination test. Through extensive simulations, we show that the proposed method performs better than the existing methods in discriminating between two lifetime distributions or two degradation models over a wide range of sample sizes. Two real examples are used to illustrate the proposed methods.

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Section: Discrimination Between Lifetime Modelsmentioning

confidence: 99%

Pairwise model discrimination with applications in lifetime distributions and degradation processes

Chen

Xiao

2019

Naval Research Logistics

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“…Koutrouvelis et al 10 and Basak and Balakrishnan 11 considered the estimation of the three‐parameter IG distribution. Using generalized inference procedure, Krishnamoorthy and Tian 12 discussed interval estimation and hypothesis testing approaches for the difference and ratio of two independent IG distributions. Ye et al 2 presented the procedures of hypothesis testing and interval estimation for the common mean of several IG populations when the scalar parameters are unknown and unequal.…”

Section: Introductionmentioning

confidence: 99%

“…Chen and Ye 15 derived an exact two‐sided

100 (1 - α) %

level CI for

μ

, and the CIs of IG quantiles were proposed based on an approximate generalized pivotal quantity (GPQ) of

μ

. The GPQ of

μ

proposed in the existing literature 2, 12–16 is approximate. We will use the probability integral transformation to get the exact GPQ of

μ

.…”

Section: Introductionmentioning

confidence: 99%

Interval estimation for inverse Gaussian distribution

Wang

Pan

et al. 2021

Quality & Reliability Eng

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In this paper, we consider interval estimation for the inverse Gaussian (IG) distribution. Using generalized pivotal quantity method, we derive the generalized confidence intervals (GCIs) for the model parameters and some quantities such as the quantile, the reliability function of the lifetime, the failure rate function, and the mean residual lifetime. We verify that the GCI of the scale parameter is the same as its commonly used exact CI. We also obtain the generalized prediction intervals (GPIs) for future failure times based on the observed failure data set. In addition, we get the GCI for the reliability of the stress–strength model when the stress and strength variables follow the IG distributions with different parameters. We compare the proposed GCIs and GPIs with the Wald CIs and bootstrap‐p CIs by simulation. The simulation results show that the proposed GCIs and GPIs are superior to the Wald CIs and the bootstrap‐p CIs in terms of the coverage probability. Finally, two examples are used to illustrate the proposed procedures.

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“…Krishnamoorthy and Tian (2008) further used generalized p-value based test to make an inference on the difference and ratio of two independent inverse Gaussian means. Subsequently, a parametric bootstrap approach for testing equality of several inverse Gaussian means under heterogeneity was applied by Ma and Tian (2009).…”

Section: Introductionmentioning

confidence: 99%

Default Bayesian testing equality of scale parameters in several inverse Gaussian distributions

Kang¹,

Kim²,

Lee³

2015

Journal of the Korean Data and Information Science Society

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This paper deals with the problem of testing about the equality of the scale parameters in several inverse Gaussian distributions. We propose default Bayesian testing procedures for the equality of the shape parameters under the reference priors. The reference prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. Therefore we propose the default Bayesian testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.

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Inferences on the difference and ratio of the means of two inverse Gaussian distributions

Cited by 24 publications

References 17 publications

Pairwise model discrimination with applications in lifetime distributions and degradation processes

Pairwise model discrimination with applications in lifetime distributions and degradation processes

Interval estimation for inverse Gaussian distribution

Default Bayesian testing equality of scale parameters in several inverse Gaussian distributions

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