Statistical Properties of Inverse Gaussian Distributions. I

Tweedie, M. C. K.

doi:10.1214/aoms/1177706964

Cited by 362 publications

(113 citation statements)

References 0 publications

Supporting

Mentioning

108

Contrasting

Unclassified

Order By: Relevance

“…If J i are i.i.d. in the sum-domain of attraction of a normal distribution, then the results of this section still hold, where now E(t) is the inverse or hitting time distribution of a Brownian motion with drift, which has an inverse Gaussian distribution Tweedie, 1957). In this case, the mixture according to E(t) is an asymptotic first-order correction to the approximation c −1 N (c) t ∼ t/ as c → ∞.…”

Section: Where F(x) = P(a(1) X) and G(s T) = P(e(t) S) Is The Distrimentioning

confidence: 74%

Extremal limit theorems for observations separated by random power law waiting times

Meerschaert

Stoev

2009

Journal of Statistical Planning and Inference

View full text Add to dashboard Cite

This paper develops extreme value theory for random observations separated by random waiting times whose exceedence probability falls off like a power law. In the case where the waiting times between observations have an infinite mean, a limit theorem is established, where the limit is comprised of an extremal process whose time index is randomized according to the non-Markovian hitting time process for a stable subordinator. The resulting limit distributions are shown to be solutions of fractional differential equations, where the order of the fractional time derivative coincides with the power law index of the waiting time. The probability that the limit process remains below a threshold is also computed. For waiting times with finite mean but infinite variance, a two-scale argument yields a fundamentally different limit process. The resulting limit is an extremal process whose time index is randomized according to the first passage time of a positively skewed stable Lévy motion with positive drift. This two-scale limit provides a second-order correction to the usual limit behavior.

show abstract

Section: Where F(x) = P(a(1) X) and G(s T) = P(e(t) S) Is The Distrimentioning

confidence: 74%

Extremal limit theorems for observations separated by random power law waiting times

Meerschaert

Stoev

2009

Journal of Statistical Planning and Inference

View full text Add to dashboard Cite

show abstract

“…The GIG distribution includes Gamma and Inverse Gamma, Inverse Gaussian and Reciprocal Inverse Gaussian distributions as its special cases. In practice, we found the three-parametric GIG form to be unnecessary, and both two-parametric special cases-Gamma (Johnson et al, 1994) and Inverse Gaussian (Johnson et al, 1994;Tweedie, 1957)-gave statistically acceptable approximations to the data on random superpositions. Approximations did not significantly improve when the third parameter was included.…”

Section: Figmentioning

confidence: 92%

Statistics of Random Protein Superpositions: p-Values for Pairwise Structure Alignment

Wrabl

Grishin

2008

Journal of Computational Biology

View full text Add to dashboard Cite

Quantification of statistical significance is essential for the interpretation of protein structural similarity. To address this, a random model for protein structure comparison was developed. Novelty of the model is threefold. First, a sample of random structure comparisons is restricted to molecules of the same size and shape as the superposition of interest. Second, careful selection of the sample and accurate modeling of shape allows approximation of the root mean square deviation (RMSD) distribution of random comparisons with a Nakagami probability density function. Third, through convolution, a second probability density function is obtained that describes the coordinate difference vector projections underlying the random distribution of RMSD. This last feature allows sampling random distributions of not only RMSD, but also any similarity score that depends on difference vector projections, such as GDT_TS score, TM score, and LiveBench 3D score. Probabilities estimated from the method correlate well with common measures of structural similarity, such as the Dali Z-score and the GDT_TS score. As a result, the p-value for a given superposition can be calculated using simple formulae depending on RMSD, radius of gyration, and thinnest molecular dimension. In addition to scoring structural similarity, p-values computed by this method can be applied to evaluation of homology modeling techniques, providing a statistically sound alternative to scores used in reference-independent evaluation of alignment quality.

show abstract

“…Tweedie (1957), Lancastar (1972), Banerjee and Bhattacharya (1976), Whitmore (1976) and Folks and Chhikara (1978) among others have done extensive work on the sampling theory and statistical applications of the inverse Gaussian distribution. Chhikara and Folks (1977) proposed the inverse Gaussian as a reliability model and suggested its applications for studying reliability aspects where the initial failure rate is high.…”

Section: Introductionmentioning

confidence: 99%

Sequential Procedures for the Point Estimation of the Mean of an Inverse Gaussian Reliability Model

Bhougal¹,

Kumar²

2017

JAC

View full text Add to dashboard Cite

In the present paper, we have considered the problem of Minimum risk point estimation of the mean of an Inverse Gaussian distribution. In case of minimum risk point estimation, consideration is given to the squared-error loss function and linear cost of sampling and in case of confidence interval estimation consideration is given to fixed width and pre-assigned coverage probability and establish the failure of the fixed sample size procedures to deal with the estimation problems. We also consider sequential estimation procedure related to the mean of an Inverse Gaussian distribution.

show abstract

Statistical Properties of Inverse Gaussian Distributions. I

Cited by 362 publications

References 0 publications

Extremal limit theorems for observations separated by random power law waiting times

Extremal limit theorems for observations separated by random power law waiting times

Statistics of Random Protein Superpositions: p-Values for Pairwise Structure Alignment

Sequential Procedures for the Point Estimation of the Mean of an Inverse Gaussian Reliability Model

Contact Info

Product

Resources

About