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1

Alternative approach to moments of order statistics from one-parameter Weibull distribution

100%

Rai P. K., Sirohi A.

Statistics in Transition new series

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2020

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vol. 21

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issue 1

169-176

EN

The Weibull distribution is used to describe various observed failures of phenomena and widely used in survival analysis and reliability theory. Sometimes it is very difficult to compute moments of such distributions due to various reasons for e.g. analytical issues, multi parameter cases etc. This study presents the computation of the moments and the expected value of the product of order statistics in the sample from the one-parameter Weibull distribution. An alternative approach in connection to survival function is used to obtain these moments and expected values. In addition the characteristic function of the above distribution is also obtained in the form of gamma functions. Further an illustration is shown to find the first two moments and expected value of the product of order statistics by using this approach.

2

Statistical properties and different methods of estimation for extended weighted inverted Rayleigh distribution

100%

Yadav A. S., Singh S. K., Singh U.

Statistics in Transition new series

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2020

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vol. 21

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issue 2

119-141

EN

The aim of this paper is to introduce a new weighted probability distribution to model the non-monotone failure rate pattern for survival data. The proposed distribution is generalized by considering inverted Rayleigh distribution as a baseline distribution called an extended weighted inverted Rayleigh distribution. Different statistical properties such as moment, quantile function, moment generating function, entropy measurement, Bonferroni and Lorenz curve, stochastic ordering and order statistics have been derived. Different estimation procedures have also been discussed to estimate the unknown parameters of the proposed probability distribution. The Monte Carlo simulation study has been conducted to compare the performances of the proposed estimators obtained through various methods of estimation. Finally, two real data sets have been used to show the applicability of the proposed model in a real-life scenario.

3

Graniczne dystrybuanty wartości ekstremalnych dla zależnych ciągów zmiennych losowych

100%

Kuźmiński Ł.

Econometrics. Ekonometria. Advances in Applied Data Analytics

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2013

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issue 2(40)

115-125

EN

In the article the outline of asymptotic theory of extreme values has been intro-duced for the application to finance, hydrology and insurance. The study includes the theo-rems and the definitions which give the possibility to appoint the limiting distribution func-tion for the distributions of maximum in three cases. The first case concerns the sequence independent random variables. The second case concerns the stationary processes of random variables for which the conditions D(un) and D’(un) are satisfied (i.e. “the extinguishing de-pendence”). The last case concerns the stationary processes for which the conditions D(un) and D’(un) are not satisfied.

4

A note on VAR for the winner’s curse

100%

Palmowski Z.

Ekonomia XXI Wieku

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2017

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issue 3 (15)

124-134

EN

This paper is an introduction to the concept and methodology of Value at Risk as a new tool for measuring exposure to the so-called winner’s curse risk. This expression was first used in the work of [Capen, Clapp, Campbell 1971] related to the oil companies, and it is usually introduced by the elementary example of the auctioning of a sealed jar with coins. The bidders cannot exactly know the value of the jar, they can just estimate it by looking at it from a distance. Usually the winner is the bidder who overestimates the value of jar the most, but actually he/she loses because of paying more than he/she receives in the jar. The same happens in insurance aggregators, but here the lowest price wins (we have then the so-called reversed auction). Traditionally, insurance companies have tried to offer insurance prices at the level of the expected value of the future costs (including all operational costs and expected profit) but now the winning company very likely is not getting enough premium to cover the assumed risk. In the case bankrupcy, this compnay will have to then face so-called winner’s curse. In this paper we analyse a few numerical examples

5

Transmuted Kumaraswamy Distribution

88%

Khan M. S., King R., Hudson I. L.

Statistics in Transition new series

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2016

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vol. 17

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issue 2

183-210

EN

The Kumaraswamy distribution is the most widely applied statistical distribution in hydrological problems and many natural phenomena. We propose a generalization of the Kumaraswamy distribution referred to as the transmuted Kumaraswamy (T K w) distribution. The new transmuted distribution is developed using the quadratic rank transmutation map studied by Shaw et al. (2009). A comprehensive account of the mathematical properties of the new distribution is provided. Explicit expressions are derived for the moments, moment generating function, entropy, mean deviation, Bonferroni and Lorenz curves, and formulated moments for order statistics. The T K w distribution parameters are estimated by using the method of maximum likelihood. Monte Carlo simulation is performed in order to investigate the performance of MLEs. The flood data and HIV/ AIDS data applications illustrate the usefulness of the proposed model.

6

Relations for moments of generalised order statistics based on Weibull–G family of distributions

88%

Athar H., Alharbi Y. F., Fawzy M. A.

Operations Research and Decisions

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2022

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vol. 32

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issue 4

EN

The Weibull distribution is one of the important distributions used in reliability theory and life-testing experiments. The generalised versions of the Weibull distribution give a more flexible model for these studies. The Weibull–G family of distributions is one of the extended versions extensively studied. In this paper, we have studied moments properties of generalised order statistics for the said distribution in terms of a single moment, product moments and characterisation. Several examples and special cases are presented. The results can be applied to all distributions belonging to this family.

7

On the improvement of paired ranked set sampling to estimate population mean

88%

Rehman S. A., Shabbir J.

Statistics in Transition new series

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2021

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vol. 22

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issue 3

193-205

EN

In ecological and environmental sampling the quantification of units is either difficult or overly demanding in terms of the time, money, workload, it requires. For this reason efficient and cost-effective sampling methods need to be devised for data collecting. The most commonly used method for this purpose is the Ranked Set Sampling (RSS). In this paper, a sampling scheme called Improved Paired Ranked Set Sampling (IPRSS) is proposed to estimate the population mean. The performance of the proposed IPRSS is evaluated under perfect and imperfect rankings. A simulation study based on selected hypothetical distributions and a real-life data set showed that IPRSS is more precise than RSS, Paired RSS (PRSS) or Extreme RSS (ERSS).

8

Poisson area-biased Ailamujia Distribution and its applications in environmental and medical sciences

75%

Aijaz A., Ain S. Q. u., Afaq A., Tripathi R.

Statistics in Transition new series

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2022

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vol. 23

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issue 3

167-184

EN

In this paper, a new Poisson area-biased Ailamujia distribution has been formulated to analyse count data. It was created by combining two distributions: the Poisson and areabiased Ailamujia distributions, using the compounding technique. Several distributional properties of the formulated distribution were studied. Its ageing characteristics were determined and expressed explicitly. A variety of diagrams were used to demonstrate the characteristics of the probability mass function (pmf) and the cumulative distribution function (cdf). The parameter of the developed model was estimated by employing the maximum likelihood estimation approach. Finally, two data sets were used to demonstrate the effectiveness of the investigated distribution.

9

On Conditional Simple Random Sample

75%

Wywiał J. L.

Statistics in Transition new series

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2014

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vol. 15

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issue 4

525–534

EN

Estimation of the population average in a finite and fixed population on the basis of the conditional simple random sampling design dependent on order statistics of the auxiliary variable is studied. The sampling scheme implementing the sampling design is proposed. The inclusion probabilities are derived. The well known Horvitz-Thompson statistic under the conditional simple random sampling designs is considered as the estimator of population mean. Moreover, it was shown that the Horvitz-Thompson estimator under some particular cases of the conditional simple random sampling design is more accurate than the ordinary mean from the simple random sample.

10

Zastosowanie teorii wartości ekstremalnychw prognozowaniu ostrzegawczym dla ciąguniezależnych zmiennych o rozkładzie normalnym

75%

Łukasz Kuźmiński Ł.

Zeszyty Naukowe Wyższej Szkoły Bankowej we Wrocławiu

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2013

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issue 2(34)

239-253

PL

Artykuł dotyczy zastosowań teorii granicznych rozkładów dla ekstremów w prognozach ostrzegawczych dla ciągu zmiennych losowych o rozkładzie normalnym. W początkowej części zawiera elementy teorii dotyczącej statystyk pozycyjnych, natomiast w dalszej przedstawione są podstawowe twierdzenia związane z teorią rozkładów typów ekstremalnych i dziedzin przyciągania. Na koniec zaprezentowano badania empiryczne, w których budowany jest model prognoz ostrzegawczych dla charakterystyk hydrologicznych. Wykorzystane w pracy dane dotyczą stanów wód na dwóch wybranych rzekach Dolnego Śląska.

EN

The work refers to the application of the theory of limit distributions for extremes in warning predictions for random variables sequences with normal distribution. The beginning of the work contains theory components concerning order statistics. In the next part of the work basic theorems connected to the theory of types of distributions and gravity areas are presented. Ultimately, empirical research is given, in which a model of warning predictions for hydrological characteristic is built. Details used in the work concern water conditions at two selected rivers of Lower Silesia.

Refine search results

Alternative approach to moments of order statistics from one-parameter Weibull distribution

Statistical properties and different methods of estimation for extended weighted inverted Rayleigh distribution

Graniczne dystrybuanty wartości ekstremalnych dla zależnych ciągów zmiennych losowych

A note on VAR for the winner’s curse

Transmuted Kumaraswamy Distribution

Relations for moments of generalised order statistics based on Weibull–G family of distributions

On the improvement of paired ranked set sampling to estimate population mean

Poisson area-biased Ailamujia Distribution and its applications in environmental and medical sciences

On Conditional Simple Random Sample

Zastosowanie teorii wartości ekstremalnychw prognozowaniu ostrzegawczym dla ciąguniezależnych zmiennych o rozkładzie normalnym