• Journal of the Korean Data and Information Science Society
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• 제10권2호
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• pp.299-311
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• 1999

In this paper the single and product moments of order statistics of the doubly truncated Rayleigh distribution are studied. Some recurrence relations of order statistics are derived. Using order statistics, also characterization of the Rayleigh distribution are derived.

• 대한수학회보
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• 제49권3호
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• pp.495-510
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• 2012

Let $X_1$, $X_2$,${\ldots}$, $X_n$ be a sequence of independent and identically distributed random variables with common distribution function $F$. Convergence rates for the moments of extremes are studied by virtue of second order regularly conditions. A unified treatment is also considered under second order von Mises conditions. Some examples are given to illustrate the results.

• International Journal of Reliability and Applications
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• 제7권2호
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• pp.187-201
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• 2006

In this paper, we derive recurrence relations for the single and product moments of progressively Type-II right censored order statistics from half logistic distribution. Next, we derive the maximum likelihood estimators (MLEs) of the location and scale parameters of the half logistic distribution. In addition, we use the setup proposed by Balakrishnan and Aggarwala (2000) to compute the approximate best linear unbiased estimates (ABLUEs) of the location and scale parameters. Finally, we point out a simulation study to compare between the efficiency of the techniques considered for the estimation.

• International Journal of Reliability and Applications
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• 제8권1호
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• pp.1-16
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• 2007

In this paper, we derive exact explicit expressions for the triple and quadruple moments of the lower record values from inverse the Weibull (IW) distribution. Next, we present and calculate the coefficients of the best linear unbiased estimates of the location and scale parameters of IW distribution (BLUEs) for different choices of the shape parameter and records size. We then use the higher order moments and the calculated BLUEs to compute the mean, variance, and the coefficients of skewness and kurtosis of certain linear functions of lower record values. By using the coefficients of the skewness and kurtosis, we develop approximate confidence intervals for the location and scale parameters of the IW distribution using Edgeworth approximate values and then compare them with the corresponding intervals constructed through Monte Carlo simulations. Finally, we apply the findings of the paper to some simulated data.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제3권2호
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• pp.157-160
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• 1999

We show the cumulants of a minimal sufficient statistics in k parameter natural exponential family by parameter function and partial parameter function. We nd the cumulants have some merits of central moments and general cumulants both. The first three cumulants are the central moments themselves and the fourth cumulant has the form related with kurtosis.

• Journal of the Korean Statistical Society
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• 제32권2호
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• pp.193-202
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• 2003

We consider a double threshold AR-ARCH type process and give sufficient conditions under which the higher-order moments exist. Geometric ergodicity and strict stationarity are also studied.

• Communications for Statistical Applications and Methods
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• 제26권3호
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• pp.239-259
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• 2019

The transmuted generalized extreme value (TGEV) distribution was first introduced by Aryal and Tsokos (Nonlinear Analysis: Theory, Methods & Applications, 71, 401-407, 2009) and applied by Nascimento et al. (Hacettepe Journal of Mathematics and Statistics, 45, 1847-1864, 2016). However, they did not give explicit expressions for all the moments, tail behaviour, quantiles, survival and risk functions and order statistics. The TGEV distribution is a more flexible model than the simple GEV distribution to model extreme or rare events because the right tail of the TGEV is heavier than the GEV. In addition the TGEV distribution can adjusted various forms of asymmetry. In this article, explicit expressions for these measures of the TGEV are obtained. The tail behavior and the survival and risk functions were determined for positive gamma, the moments for nonzero gamma and the moment generating function for zero gamma. The performance of the maximum likelihood estimators (MLEs) of the TGEV parameters were tested through a series of Monte Carlo simulation experiments. In addition, the model was used to fit three real data sets related to financial returns.

• Communications for Statistical Applications and Methods
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• 제21권2호
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• pp.147-160
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• 2014

In this paper, we introduce the exponentiated Weibull-geometric (EWG) distribution which generalizes two-parameter exponentiated Weibull (EW) distribution introduced by Mudholkar et al. (1995). This proposed distribution is obtained by compounding the exponentiated Weibull with geometric distribution. We derive its cumulative distribution function (CDF), hazard function and the density of the order statistics and calculate expressions for its moments and the moments of the order statistics. The hazard function of the EWG distribution can be decreasing, increasing or bathtub-shaped among others. Also, we give expressions for the Renyi and Shannon entropies. The maximum likelihood estimation is obtained by using EM-algorithm (Dempster et al., 1977; McLachlan and Krishnan, 1997). We can obtain the Bayesian estimation by using Gibbs sampler with Metropolis-Hastings algorithm. Also, we give application with real data set to show the flexibility of the EWG distribution. Finally, summary and discussion are mentioned.

• 대한수학회논문집
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• 제21권2호
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• pp.375-384
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• 2006

We consider a class of bilinear models with periodic regime switching and find easy-to-check sufficient conditions that ensures the existence of a stationary process obtained from given difference equation. Existence of a higher order moments is examined.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.119-132
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• 2006

This paper presents an approach for using right-truncated exponentially distributed random variables to model activity times in stochastic activity networks. The advantages of using the right-truncated exponential distribution are discussed. The moments of a project completion time using the proposed distribution are derived and compared with other estimated moments in literature.