Weighted Cumulative Residual (Past) Inaccuracy For Minimum (Maximum) of Order Statistics

In this paper, we propose a measure of weighted cumulative residual inaccuracy between survival function of the first-order statistic and parent survival function $\bar{F}$. We also consider weighted cumulative inaccuracy measure between distribution of the last- order statistic and parent distribution $F$. For these concepts, we obtain some reliability properties and characterization results such as relationships with other functions, bounds, stochastic ordering and effect of linear transformation. Dynamic versions of these weighted measures are considered.

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Characterization of generalized Gamma-Lindley distribution using truncated moments of order statistics

Mathematica Slovaca ◽

10.1515/ms-2017-0481 ◽

2021 ◽

Vol 71 (2) ◽

pp. 455-474

Author(s):

Dorsaf Laribi ◽

Afif Masmoudi ◽

Imen Boutouria

Keyword(s):

Order Statistics ◽

Survival Function ◽

Lindley Distribution ◽

Underlying Distribution ◽

First Order ◽

New Class ◽

Generalized Gamma ◽

Special Cases ◽

Two Parameters

Abstract Having only two parameters, the Gamma-Lindley distribution does not provide enough flexibility for analyzing different types of lifetime data. From this perspective, in order to further enhance its flexibility, we set forward in this paper a new class of distributions named Generalized Gamma-Lindley distribution with four parameters. Its construction is based on certain mixtures of Gamma and Lindley distributions. The truncated moment, as a characterization method, has drawn a little attention in the statistical literature over the great popularity of the classical methods. We attempt to prove that the Generalized Gamma-Lindley distribution is characterized by its truncated moment of the first order statistics. This method rests upon finding a survival function of a distribution, that is a solution of a first order differential equation. This characterization includes as special cases: Gamma, Lindley, Exponential, Gamma-Lindley and Weighted Lindley distributions. Finally, a simulation study is performed to help the reader check whether the available data follow the underlying distribution.

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Characterizations Based on Cumulative Residual Entropy of First-Order Statistics

Communication in Statistics- Theory and Methods ◽

10.1080/03610920903324841 ◽

2010 ◽

Vol 39 (20) ◽

pp. 3645-3651 ◽

Cited By ~ 22

Author(s):

S. Baratpour

Keyword(s):

Order Statistics ◽

Residual Entropy ◽

First Order ◽

Cumulative Residual Entropy ◽

Cumulative Residual

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Experimental Investigation of the First-order Statistics of Stokes Parameters in Speckle Fields

Optica Acta International Journal of Optics ◽

10.1080/713820756 ◽

1982 ◽

Vol 29 (10) ◽

pp. 1395-1400 ◽

Cited By ~ 12

Author(s):

P.F. Steeger ◽

A.F. Fercher

Keyword(s):

Experimental Investigation ◽

Order Statistics ◽

Stokes Parameters ◽

First Order

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Choice, Order Statistics and the Distribution of Earnings

Journal of Income Distribution ◽

10.25071/1874-6322.670 ◽

1997 ◽

Author(s):

Michael Sattinger

Keyword(s):

Order Statistics ◽

Order Statistic ◽

Occupational Choice ◽

Earnings Inequality ◽

Limiting Distribution ◽

Asymptotic Results ◽

Expected Earnings

This paper analyzes the distribution of earnings as being generated by workers choosing among occupations on the basis of earnings maximization. A worker’s earnings then have characteristics of an order statistic. The extension to multiple occupations leads to the revision results from A.D. Roy’s two-occupation case. An additional occupation raises expected earnings while in general reducing earnings inequality. Asymptotic results from order statistics suggest that the process of occupational choice determines a limiting distribution of earnings independently of underlying distributions of occupational abilities.

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On cumulative residual entropy of progressively censored order statistics

Statistics & Probability Letters ◽

10.1016/j.spl.2018.03.008 ◽

2018 ◽

Vol 139 ◽

pp. 47-52

Author(s):

Z.A. Abo-Eleneen ◽

B. Almohaimeed ◽

H.K.T. Ng

Keyword(s):

Order Statistics ◽

Residual Entropy ◽

Cumulative Residual Entropy ◽

Cumulative Residual

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Modeling of First-Order Statistics of the MIMO Dual Polarized Channel at 2 GHz for Land Mobile Satellite Systems Under Tree Shadowing

IEEE Transactions on Antennas and Propagation ◽

10.1109/tap.2014.2346186 ◽

2014 ◽

Vol 62 (10) ◽

pp. 5410-5415 ◽

Cited By ~ 13

Author(s):

Charilaos Kourogiorgas ◽

Milan Kvicera ◽

Dimitrios Skraparlis ◽

Tomas Korinek ◽

Vasileios K. Sakarellos ◽

...

Keyword(s):

Order Statistics ◽

Satellite Systems ◽

First Order ◽

Dual Polarized ◽

Mobile Satellite ◽

Mobile Satellite Systems

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Higher Order Moments of the Order Statistics for the Rectangular, Exponential, Gamma and Weibull Distributions

European Journal of Mathematics and Statistics ◽

10.24018/ejmath.2021.2.3.23 ◽

2021 ◽

Vol 2 (3) ◽

pp. 61-76

Author(s):

Sampath Kumar ◽

V. V. HaraGopal

Keyword(s):

Image Analysis ◽

Order Statistics ◽

Order Statistic ◽

Higher Order ◽

Weibull Distributions ◽

Higher Order Moments

In this paper we discuss the problem of Higher Order Moments for the order Statistics for the Rectangular, Exponential, Gamma and Weibull distributions by finding the order statistic distributions for the base distribution and modified distributions, the base distribution is to deduce the corresponding distribution by the polynomial modifier. These higher order moments are very much useful in most of the Data sciences and Image analysis.

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