Characterizing the geometric distribution using expectations of order statistics

1987 ◽  
Vol 24 (02) ◽  
pp. 534-539 ◽  
Author(s):  
A. C. Dallas
Keyword(s):  
Order Statistics ◽  
Conditional Expectation ◽  
Geometric Distribution ◽  
Discrete Distributions

The constancy of the conditional expectation of some appropriate functions of order statistics on some others, is used to characterize the geometric distribution among the discrete distributions.

Characterizing the geometric distribution using expectations of order statistics

1987 ◽  
Vol 24 (2) ◽  
pp. 534-539 ◽  
Author(s):  
A. C. Dallas
Keyword(s):  
Order Statistics ◽  
Conditional Expectation ◽  
Geometric Distribution ◽  
Discrete Distributions

The constancy of the conditional expectation of some appropriate functions of order statistics on some others, is used to characterize the geometric distribution among the discrete distributions.

On characterizations of the geometric distribution by independence of functions of order statistics

1986 ◽  
Vol 23 (1) ◽  
pp. 227-232 ◽  
Author(s):  
R. C. Srivastava
Keyword(s):  
Order Statistics ◽  
Geometric Distribution ◽  
Random Variables ◽  
Weak Form ◽  
Discrete Distributions ◽  
Independence Properties

Let X1, · ··, Xn, n ≧ 2 be i.i.d. random variables having a geometric distribution, and let Y1 ≦ Y2 ≦ · ·· ≦ Yn denote the corresponding order statistics. Define Rn = Yn – Y1 and Zn = Σj=2n (Υj – Y1). Then it is well known that (i) Y, and Rn are independent and (ii) Y1 and Zn are independent. In this paper, we show that a very weak form of each of these independence properties is a characterizing property of the geometric distribution in the class of discrete distributions.

On characterizations of the geometric distribution by independence of functions of order statistics

1986 ◽  
Vol 23 (01) ◽  
pp. 227-232
Author(s):  
R. C. Srivastava
Keyword(s):  
Order Statistics ◽  
Geometric Distribution ◽  
Random Variables ◽  
Weak Form ◽  
Discrete Distributions ◽  
Independence Properties

Let X1, · ··, X n , n ≧ 2 be i.i.d. random variables having a geometric distribution, and let Y 1 ≦ Y 2 ≦ · ·· ≦ Y n denote the corresponding order statistics. Define Rn = Yn – Y 1 and Z n = Σ j=2 n (Υ j – Y1). Then it is well known that (i) Y, and Rn are independent and (ii) Y 1 and Zn are independent. In this paper, we show that a very weak form of each of these independence properties is a characterizing property of the geometric distribution in the class of discrete distributions.

scholarly journals Modifying Bradley–Terry and other ranking models to allow ties

2020 ◽  
Author(s):  
Rose Baker ◽  
Philip Scarf
Keyword(s):  
Order Statistics ◽  
Exponential Distribution ◽  
Geometric Distribution ◽  
Discrete Distributions ◽  
Ranking Models

Abstract Models derived from distributions of order-statistics are useful for modelling ranked data. The well-known Bradley–Terry (BT) and Plackett–Luce (PL) models can be derived from the order statistics of the exponential distribution but cannot handle ties. However, ties often occur in sports, and the ability to accommodate them leads to more useful ranking models. In this paper, we use discrete distributions, principally the geometric distribution, to obtain modified BT and PL models and some others that allow tied ranks. Our methodology is introduced for some mathematically tractable and some less tractable distributions and is illustrated using test match cricket.

scholarly journals On the quotient moment of lower generalized order statistics and characterization

2015 ◽  
Vol 11 (1) ◽  
pp. 73-89
Author(s):  
Devendra Kumar
Keyword(s):  
Order Statistics ◽  
Recurrence Relation ◽  
Conditional Expectation ◽  
General Class ◽  
Recurrence Relations ◽  
Generalized Order Statistics ◽  
Lower Records ◽  
Moments Of Order Statistics ◽  
Generalized Order

Abstract In this paper we consider general class of distribution. Recurrence relations satisfied by the quotient moments and conditional quotient moments of lower generalized order statistics for a general class of distribution are derived. Further the results are deduced for quotient moments of order statistics and lower records and characterization of this distribution by considering the recurrence relation of conditional expectation for general class of distribution satisfied by the quotient moment of the lower generalized order statistics.

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