Characterizations of distributions of exponential or geometric type by the integrated lack of memory property and record values

Witte, Hans-Jüurgen

doi:10.1016/0167-9473(90)90008-6

Cited by 6 publications

(2 citation statements)

References 13 publications

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“…In the first place, we extend the characterizations of exponential and geometrical distributions given in Witte (1988Witte ( ), (1990 to the non-stationary model described in Section 1. Note here that, whenever F; = F for all n~0, this model is identical to the classical stationary model.…”

Section: Characterizations Based On the Equidistribution Of R; -R; -Imentioning

confidence: 99%

Some characterizations of exponential or geometric distributions in a non-stationary record value model

Witte

1993

Journal of Applied Probability

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Let {Fn}n ≧ 0 be a sequence of c.d.f. and let {Rn}n ≧ 1 be the sequence of record values in a non-stationary record model where after the (n − 1)th record the population is distributed according to Fn. Then the equidistribution of the nth population and the record increment Rn – Rn– 1 (i.e. Rn – Rn– 1~ Fn) characterizes Fn to have an exponentially decreasing hazard function. To be more precise Fn is the exponential distribution if the support of Rn– 1 generates a dense subgroup in and otherwise the entity of all possible solutions can be obtained in the following way: let for simplicity the above additive subgroup be any c.d.f. F satisfying F(0) = 0, F(1) < 1 can be chosen arbitrarily. Setting λ = – log(1 – F(1)), Fn(x) = 1 – F(x – [x])exp(–λ [x]) is an admissible solution coinciding with F on the interval [0, 1] ([x] denotes the integer part of x). Simple additional assumptions ensuring that Fn is either exponential or geometric are given. Similar results for exponential or geometric tail distributions based on the independence of Rn– 1 and Rn – Rn– 1 are proved.

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Section: Characterizations Based On the Equidistribution Of R; -R; -Imentioning

confidence: 99%

Some characterizations of exponential or geometric distributions in a non-stationary record value model

Witte

1993

Journal of Applied Probability

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“…There are some characterization properties of standard distributions using the properties of order statistics (see, e.g., Pfeifer [8], Bairamov and Ozkal [9], Huang and Su [10], Beg et al [11], Kayid and Izadkhah [12], Akbari et al [13], Hu and Lin [14], and Betsch and Ebner [15]). Further-more, there are several characterization results of reputable probability distributions derived by the properties of record statistics (see, e.g., Witte [16], Kamps [17], Franco and Ruiz [18], Wesolowski and Ahsanullah [19], Nagaraja and Barlevy [20], Balakrishnan and Stepanov [21], Baratpour et al [22], and Ahmadi [23]).…”

Section: Introductionmentioning

confidence: 99%

Characterizations of Probability Distribution by Some Sequential Relative Reliability Measures: An Application of Completeness in a Hilbert Space

Shrahili

Kayid

2022

Journal of Function Spaces

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In this paper, by means of the concept of completeness in functional analysis, we characterize probability distributions using several relative measures of residual life of an item at independent sequences of random times. These sequences are the order statistics and the record statistics of a random sequence of times. The reliability quantities of the mean residual life, the vitality function, and the survival function are considered to construct the main characteristics of distributions.

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Characterizations of discrete distributions based on conditional expectations of record values

Franco

Ruiz

2001

Statistical Papers

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Characterizations of distributions of exponential or geometric type by the integrated lack of memory property and record values

Cited by 6 publications

References 13 publications

Some characterizations of exponential or geometric distributions in a non-stationary record value model

Some characterizations of exponential or geometric distributions in a non-stationary record value model

Characterizations of Probability Distribution by Some Sequential Relative Reliability Measures: An Application of Completeness in a Hilbert Space

Characterizations of discrete distributions based on conditional expectations of record values

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