Estimation of the location and scale parameters of a power function distribution based on a selected number of order statistics
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Abstract:
Suppose are the order statistics of a random sample of size n from a power-function distribution known. The best linear unbiased estimators of α and/or β based on k(≤ n) order statistics are obtained. It is found that the efficiencies are very high if (x(l), x(2)) or (x(l), x(n)) (depending on the value of γ) Is used for estimating α when β is known and (x(l), x(n)) is used for jointly estimating α and β. In estimating β when α is known, x(n) is proved to be the optimum order statistic.Keywords:
Statistic
Power function
Location parameter
Value (mathematics)
Scale parameter
A new class of statistics obtained by ordering the absolute values of the observations arising from absolutely continuous distributions which are symmetrically distributed about zero is introduced in this paper. The statistics generated by the above method are named as absolved order statistics (AOS) of the given sample. The association of the distribution of these statistics with the distribution of order statistics arising from the folded form of the parental density about zero is outlined. The vector of AOS is proved to be a minimal sufficient statistic for the class Fθ(1) of all absolutely continuous distributions which are symmetrically distributed about zero. A method of estimation of the scale parameter of any distribution belonging to Fθ(1) using AOS is described. Illustration on the advantage of the above method of estimation is described for the distributions such as (i) logistic, (ii) normal, and (iii) double Weibull. A more realistic censoring scheme involving AOS as well is discussed in this paper. We have derived the U-statistic estimator based on AOS for the scale parameter σ of any distribution f(x,σ)∈Fθ(1) using the best linear unbiased estimate (BLUE) based on AOS of a preliminary sample as kernel. We have illustrated the performance of this estimator with an U-statistic generated from BLUE based on order statistics for each of (i) logistic (ii) normal and (iii) double Weibull distributions.
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Abstract Estimates of the location and scale parameters, linear in the order statistics of a Type II censored or complete sample, from a continuous symmetric unimodal distribution satisfying certain conditions are obtained. Their coefficients are explicit functions of the expectations of the order statistics or population quantiles from the known parameter‐free standardized distribution. Linear estimates with simpler coefficients are also obtained. The theorems state the complete sample case, and the singly and doubly censored cases. The more general case, the multiple censoring, is an extension of these cases and is indicated. All the estimates obtained are asymptotically efficient in the strict sense.
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AbstractThis paper deals with estimating the location and the scale parameters of the extreme value distribution when the sample size is very large, using sample quantiles. An estimator is given for the location parameter when the scale parameter is known, based on one or more (up to 15) order statistics. Also given is an estimator for the scale parameter when the location parameter is known, built on two order statistics. An iterative procedure is utilized to estimate the parameters when both are unknown, using two order statistics. The problem of estimating the percentage point is also dealt with, and a comparison with Lieblein's method is included.
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Abtsrcat In this work, we obtain the best linear unbiased estimator based on order statistics for the scale parameter of skew-normal distribution for some known values of the shape parameter. We also propose a technique for estimating the scale parameter of skew-normal distribution by U-statistics based on best linear functions of order statistics as kernels. The efficiency comparison of the proposed U-statistics with the maximum likelihood esti- mator is also carried out.
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