Lower Record Values Research Articles

Characterization of Distribution by Conditional Expectation of Lower Record Values

It is widely known that the problem of characterizing a distribution an important problem which has recently attracted the attention of many researchers. Thus various characterizations have been established in many directions. In this paper, a general form of continuous probability distribution is characterized through conditional expectation of contrast of lower record statistics, conditioned on a non-adjacent record statistics and some of its deductions are also discussed.

Analysis of Inverse Weibull Distribution based on Record Values

In this research paper, the estimates of the parameters of Inverse Weibull distribution (IWD) are obtained from lower record values by using Lloyd's Method and Gupta's Method. The comparisons b etween the performances of both the estimation methods, for location and scale parameters of IWD, have been made in terms of relative efficiency numerically and graphically. The study explored that relative efficiency of Gupta's estimators for location and scale para meters of IWD increases as the value of shape parameter increases.

On some properties of Makeham distribution using generalized record values and its characterization

In this paper, we derive some recurrence relations satisfied by single and product moments of generalized upper record values arising from the Makeham distribution. We obtain similar results for the inverse Makeham distribution using generalized lower record values. Further, we have identified some of these recurrence relations and other properties of generalized record values which characterize Makeham and inverse Makeham distributions.

On Moments of Lower Generalized Order Statistics from Exponentiated Lomax Distribution

SYNOPTIC ABSTRACT In this study we obtain explicit expressions and some recurrence relations for single and product moments of lower generalized order statistics from the exponentiated Lomax distribution. The results for order statistics and lower record value from the relation are derived. Further, a characterizing result of this distribution on using the conditional moment of lower generalized order statistics is discussed.

MOMENTS OF LOWER GENERALIZED ORDER STATISTICS FROM DOUBLY TRUNCATED CONTINUOUS DISTRIBUTIONS AND CHARACTERIZATIONS

In this paper, we derive recurrence relations for moments of lower generalized order statistics within a class of doubly truncated distributions. Inverse Weibull, exponentiated Weibull, power function, exponentiated Pareto, exponentiated gamma, generalized exponential, exponentiated log-logistic, generalized inverse Weibull, extended type I generalized logistic, logistic and Gumble distributions are given as illustrative examples. Further, recurrence relations for moments of order statistics and lower record values are obtained as special cases of the lower generalized order statistics, also two theorems for characterizing the general form of distribution based on single moments of lower generalized order statistics are given.

Asymptotic distributions of order statistics and record values arising from the class of beta-generated distributions

In this paper, we show that both the class of beta-generated distributions GF and its base distribution F belong to the same domain of maximal (or minimal or upper record value or lower record value) attraction. Moreover, it is shown that the weak convergence of any non-extreme order statistic (central or intermediate order statistic), based on a base distribution F, to a non-degenerate limit type implies the weak convergence of GF to a non-degenerate limit type. The relations between the two limit types are deduced.

A CHARACTERIZATION OF THE POWER FUNCTION DISTRIBUTION BY INDEPENDENT PROPERTY OF LOWER RECORD VALUES

We prove a characterization of the power function distribution by lower record values. We prove that $F(x)

On moments of k-th record values from the linear exponential distribution

Explicit formulae for single, central, and product moments of k-th upper and lower record values from the linear exponential distribution are given. The limited moments and the mean residual life function are also investigated. Moreover, recurrence relations for moments of k-th upper and lower record values from this distribution are derived.

Recurrence Relations for the Moments of Generalized Inverse Weibull Distribution Based on Lower Records and a Characterization

Abstract—In this study we derive exact expressions and some recurrence relations for single and product moments of lower record values from generalized inverse Weibull distribution. Two theorems on characterization of the generalized inverse Weibull distribution based on conditional expectation of function and the recurrence relation for single moments of lower records are also presented.

Estimation for Two-Parameter Generalized Exponential Distribution Based on Records

This paper derives maximum likelihood estimators (MLEs) and some approximate MLEs (AMLEs) of unknown parameters of the generalized exponential distribution when data are lower record values. We derive approximate Bayes estimators through importance sampling and obtain corresponding Bayes predictive intervals for unknown parameters for lower record values from the generalized exponential distribution. For illustrative purposes, we examine the validity of the proposed estimation method by using real and simulated data.

Bayesian Inference of Generalized Exponential Distribution Based on Lower Record Values

SYNOPTIC ABSTRACT This article addresses the problem of frequentist and Bayesian estimation of the parameters of the generalized exponential distribution (GED) using lower record values. The maximum likelihood estimates (MLE) and the Bayes estimates based on lower records are derived for the unknown parameters of the GED. We consider the Bayes estimators of the unknown parameters under the assumption of gamma priors on both the shape and the scale parameters. The Bayes estimators cannot be obtained in explicit forms. The Bayesian estimation of the parameters of the GED has been studied with respect to both symmetric and asymmetric loss functions. We have also derived the Bayes interval of this distribution and discussed the Bayesian prediction intervals of the future record values based on the observed record values. Monte Carlo simulations are performed to compare the performances of the proposed methods, and one dataset has been analyzed for illustrative purposes.

Relations for Marginal and Joint Moment Generating Functions of Marshall-Olkin Extended Logistic Distribution Based on Lower Generalized Order Statistics and Characterization

SYNOPTIC ABSTRACT In this study we give exact expressions and some recurrence relations for marginal and joint moment generating functions of lower generalized order statistics from Marshall-Olkin extended logistic distribution. The results for order statistics and lower record values are deduced from the relations derived. Further, a characterization of this distribution by considering recurrence relations for marginal moment generating functions of the lower generalized order statistics is presented.

Reconstruction of the past lower record values in a proportional reversed hazard rate model

In this paper, the situation in which some lower records from a proportional reversed hazard rate model (PRHRM) are lost at the beginning of the experiment is considered. The reconstruction problem of the past lower records based on observed records from a PRHRM is discussed. Several various methods are used to obtain point reconstructors. More details are given for the Fréchet distribution. Three reconstruction intervals are also obtained and compared in the sense of the expected width for the case of Fréchet distribution. A data set representing the annual flood loss is applied to illustrate the proposed procedure in this paper. Eventually, some concluding remarks are presented.

The gamma-exponentiated exponential distribution

In this paper, we introduce a new distribution generated by gamma random variables. We show that this distribution includes as a special case the distribution of the lower record value from a sequence of i.i.d. random variables from a population with the exponentiated (generalized) exponential distribution. The properties of this distribution are derived and the estimation of the model parameters is discussed. Some applications to real data sets are finally presented for illustration.

Characterizations of symmetric distributions based on Rényi entropy

It is proved that the equality of Rényi entropies of upper and lower order statistics as well as upper and lower k-records is a characteristic property of symmetric distributions. Also, for Farlie–Gumbel–Morgenstern (FGM) family, it is shown that under some conditions the equality of entropies of concomitants of upper and lower order statistics as well as concomitants of upper and lower record values is a characteristic property for the uniform distribution.

Some results on conditional expectations of lower record values

In this paper, we propose a measure for obtaining the expectation of time between two lower k-records under the condition that the greater one is given. Several properties of the proposed measure are derived. Some characterization results and stochastic comparisons based on the new measure are also provided.

Coherent random permutations with biased record statistics

We consider random permutations that are defined coherently for all values of n , and for each n have a probability distribution which is conditionally uniform given the set of upper and lower record values. Our central example is a two-parameter family of random permutations that are conditionally uniform given the counts of upper and lower records. This family may be seen as an interpolation between two versions of Ewens’ distribution. We discuss characterisations of the conditionally uniform permutations, their asymptotic properties, constructions and relations to random compositions.

Exact Moments of Lower Generalized Order Statistics from Power Function Distribution

Abtsrcat Order statistics, record values and several other model of ordered random variables can be viewed as special case of generalized order statistics ( gos) [Kamps, 1995]. Pawlas and Szynal (2001) introduced the con-cept of lower generalized order statistics ( lgos) to enable a common approach to descending ordered rv's like reversed order statistics and lower record values. The work of Burkschat et al. (2003) may also be seen for dual (lower) generalized order statistics. In this paper simple expressions for single and product moments of lower generalized order statistics from power function distribution have been obtained. Further, some important deductions and computational works are carried out.

Record Values from the Inverse Weibull Lifetime Model: Different Methods of Estimation

In this paper, we use the lower record values from the inverse Weibull distribution (IWD) to develop and discuss different methods of estimation in two different cases, 1) when the shape parameter is known and 2) when both of the shape and scale parameters are unknown. First, we derive the best linear unbiased estimate (BLUE) of the scale parameter of the IWD. To compare the different methods of estimation, we present the results of Sultan (2007) for calculating the best linear unbiased estimates (BLUEs) of the location and scale parameters of IWD. Second, we derive the maximum likelihood estimates (MLEs) of the location and scale parameters. Further, we discuss some properties of the MLEs of the location and scale parameters. To compare the different estimates we calculate the relative efficiency between the obtained estimates. Finally, we propose some numerical illustrations by using Monte Carlo simulations and apply the findings of the paper to some simulated data.

Asymptotic Distributions of Order Statistics and Record Values Under the Marshall–Olkin Parametrization Operation

The Marshall and Olkin (1997) parametrization operation is given by where F 1 is a given distribution function and α > 0, = 1 − α. In this article, we show that both F α = 𝒫α(F 1) and the generating distribution F 1 belong to the same domain of maximal (minimal) (upper record value) (lower record value) attraction. Moreover, it is shown that the weak convergence of any non extreme order statistic (order statistic with variable rank) based on F 1, under given normalizing constants, to a non degenerate limit type implies that the same non extreme order statistic based on the family F α = 𝒫α(F 1), α≠1, under the same normalizing constants, does not converge to any non degenerate distribution and vice versa.