Asymptotic behavior of the record values in a stationary Gaussian sequence, with applications

Abstract In this paper, we study the limit distributions of upper and lower record values of a stationary Gaussian sequence under an equi-correlated set up. Moreover, the class of limit distribution functions (df’s) of the joint upper (and the lower) record values of a stationary Gaussian sequence is fully characterized. As an application of this result, the sufficient conditions for the weak convergence of the record quasi-range, record quasi-mid-range, record extremal quasi-quotient and record extremal quasi-product are obtained. Moreover, the classes of the non-degenerate limit df’s of these statistics are derived.

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Some Characterization and Relations Based on K-th Lower Record Values

The Open Statistics & Probability Journal ◽

10.2174/1876527001607010036 ◽

2016 ◽

Vol 7 (1) ◽

pp. 36-44

Author(s):

Ali A. Al-Shomrani

Keyword(s):

Conditional Expectation ◽

Recurrence Relations ◽

Sufficient Conditions ◽

Random Variable ◽

Record Values ◽

Distribution Functions ◽

Conditional Expectations ◽

Lower Record ◽

Lower Record Values ◽

Necessary And Sufficient

In this paper, we obtain certain expressions and recurrence relations for two general classes of distributions based on some conditional expectations of k-th lower record values. We consider the necessary and sufficient conditions such that these conditional expectations hold for some distribution functions. Furthermore, an expression of conditional expectation of other general class of distributions through truncated moments of some random variable is considered. Some distributions as examples of these general classes are shown in Tables1and2accordingly.

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Asymptotic behavior of the records of multivariate random sequences in a norm sense

Mathematica Slovaca ◽

10.1515/ms-2017-0442 ◽

2020 ◽

Vol 70 (6) ◽

pp. 1457-1468

Author(s):

Haroon M. Barakat ◽

M. H. Harpy

Keyword(s):

Asymptotic Behavior ◽

Weak Convergence ◽

Sufficient Conditions ◽

Record Values ◽

Necessary And Sufficient Conditions ◽

Random Sequences ◽

Necessary And Sufficient

AbstractIn this paper, we investigate the asymptotic behavior of the multivariate record values by using the Reduced Ordering Principle (R-ordering). Necessary and sufficient conditions for weak convergence of the multivariate record values based on sup-norm are determined. Some illustrative examples are given.

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Limit Theorems for Bivariate Generalised Order Statistics in Stationary Gaussian Sequences with Random Sample Sizes

Proceedings of the Latvian Academy of Sciences. Section B. Natural, Exact, and Applied Sciences. ◽

10.2478/prolas-2019-0080 ◽

2019 ◽

Vol 73 (6) ◽

pp. 525-532

Author(s):

Fatma Hashem Essawe ◽

Mohamed Abd Elgawad ◽

Haroon Mohamed Barakat ◽

Hui Zhao

Keyword(s):

Weak Convergence ◽

Order Statistics ◽

Random Sample ◽

Limit Theorems ◽

Sufficient Conditions ◽

Distribution Functions ◽

Random Sample Size ◽

Lower Upper ◽

Set Up ◽

Random Indices

Abstract In this paper, we study the limit distribution functions of the (lower-lower), (upper-upper) and (lower-upper) extreme and central-central m-generalised order statistics (m–GOS) of stationary Gaussian sequences under an equi-correlated set up, when the random sample size is assumed to converge weakly and independent of the basic variables. Moreover, sufficient conditions for a weak convergence of generalised quasi-range with random indices are obtained.

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Bayes Estimation of Topp-Leone Distribution Under Symmetric Entropy Loss Function Based on Lower Record Values

Science Journal of Applied Mathematics and Statistics ◽

10.11648/j.sjams.20160406.16 ◽

2016 ◽

Vol 4 (6) ◽

pp. 284 ◽

Cited By ~ 1

Author(s):

Lanping Li

Keyword(s):

Loss Function ◽

Record Values ◽

Bayes Estimation ◽

Entropy Loss ◽

Lower Record ◽

Lower Record Values

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Interval estimation for proportional reversed hazard family based on lower record values

Statistics & Probability Letters ◽

10.1016/j.spl.2014.12.019 ◽

2015 ◽

Vol 98 ◽

pp. 115-122 ◽

Cited By ~ 11

Author(s):

Bing Xing Wang ◽

Keming Yu ◽

Frank P.A. Coolen

Keyword(s):

Interval Estimation ◽

Record Values ◽

Lower Record ◽

Lower Record Values ◽

Family Based

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A Characterization and Recurrence Relations of Moments of the Size-Biased Power Function Distribution by Lower Record Values

International Journal of Statistics and Probability ◽

10.5539/ijsp.v7n5p1 ◽

2018 ◽

Vol 7 (5) ◽

pp. 1

Author(s):

Shakila Bashir ◽

Mujahid Rasul

Keyword(s):

Power Function ◽

Recurrence Relations ◽

Survival Function ◽

Joint Probability ◽

Record Values ◽

Cumulative Distribution ◽

Function Distribution ◽

Power Function Distribution ◽

Lower Record ◽

Lower Record Values

A variety of research papers have been published on record values from various continuous distributions. This paper investigated lower record values from the size-biased power function distribution (LR-SPFD). Some basic properties including moments, skewness, kurtosis, Shannon entropy, cumulative distribution function, survival function and hazard function of the lower record values from SPFD have been discussed. The joint probability density function (pdf) of $n^{th}$ and $m^{th}$ lower record values from SPFD is developed. Recurrence relations of the single and product moments of the LR-SPFD have been derived. A characterization of the lower record values from SPFD is also developed.

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