On some properties of Kies distribution

Kumar, C. Satheesh; Dharmaja, S. H. S.

doi:10.1007/s40300-013-0018-8

Cited by 18 publications

(4 citation statements)

References 14 publications

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“…We shall denote by p(x; λ, β) the inverse function of (8) in the domain (0, ∞). Note that it is well defined since function (8) increases from P (0; λ, β) = 0 to P (∞; λ, β) = ∞.…”

Section: Min-kies Distributionmentioning

confidence: 99%

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On min- and max-Kies families: distributional properties and saturation in Hausdorff sense

Zaevski,

Kyurkchiev

2024

Modern Stochastics: Theory and Applications

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The purpose of this paper is to explore two probability distributions originating from the Kies distribution defined on an arbitrary domain. The first one describes the minimum of several Kies random variables whereas the second one is for their maximum – they are named min- and max-Kies, respectively. The properties of the min-Kies distribution are studied in details, and later some duality arguments are used to examine the max variant. Also the saturations in the Hausdorff sense are investigated. Some numerical experiments are provided.

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Section: Min-kies Distributionmentioning

confidence: 99%

“…This way its domain turns from the positive real half-line (Weibull) to the interval (0, 1). Analogously, the transformation t = by+a y+1 ⇔ y = t−a b−t , a < b, leads to the Kies distribution on the interval (a, b)we refer to [8,14,19].…”

Section: Introductionmentioning

confidence: 99%

On min- and max-Kies families: distributional properties and saturation in Hausdorff sense

Zaevski,

Kyurkchiev

2024

Modern Stochastics: Theory and Applications

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“…Let X be a random variable from the Kies distribution, the associated probability density function (PDF), cumulative distribution function (CDF), survival function (SF) and hazard rate function (HRF) can be expressed respectively as Like traditional exponential, Weibull and gamma distributions, the Kies distribution also features decreasing, increasing, and bathtub-shaped hazard rates, respectively (Satheesh Kumar and Dharmaja 19,20 ), which make it very flexible in data fitting. Especially, the bathtub HRF of the Kies model may be useful in modeling different data and helps to associate this model as an useful alternative to traditional distributions like gamma, Weibull, modified Weibull, etc.…”

Section: Introductionmentioning

confidence: 99%

“…Like traditional exponential, Weibull and gamma distributions, the Kies distribution also features decreasing, increasing, and bathtub-shaped hazard rates, respectively (Satheesh Kumar and Dharmaja 19,20 ), which make it very flexible in data fitting. Especially, the bathtub HRF of the Kies model may be useful in modeling different data and helps to associate this model as an useful alternative to traditional distributions like gamma, Weibull, modified Weibull, etc.…”

Section: Introductionmentioning

confidence: 99%

Estimation for Kies distribution with generalized progressive hybrid censoring under partially observed competing risks model

Prakash

Tripathi

Wang

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part O:

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In this paper, estimation of a competing risks model is discussed with partially observed modes of failure. When latent lifetimes of competing risks follow the Kies distribution under a generalized progressive hybrid censoring, estimation of the unknown parameters is explored under non-order and order restrictions via classical and Bayesian approaches, respectively. The uniqueness and existence of maximum likelihood estimators of parameters are established, and subsequently interval estimators are also derived. Bayesian estimates as well as highest posterior density credible intervals are developed for the model parameters. In addition, when extra order information for the competing risks parameters is available, classical and Bayesian estimates are also established. Extensive simulation studies are conducted to investigate the performance of different methods, and a numerical example is also presented for illustrative purposes.

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