On a conjecture of Kakosyan,Klebanov and Melamed

Suppose X₁, X₂, ..., X_m is a random sample of size m from a population with probability density function f(x), x>0 and let X_1,m<...m,m be the corresponding order statistics. We assume m as an integer valued random variable with P(m=k)=p(1?p)^k?1, k=1, 2, ... and 0 and n X_1,n for fixed n characterizes the exponential distribution. In this paper we prove that under the assumption of monotone hazard rate the identical distribution of and (n?r+1) (X_r,n?X_r?1,n) for some fixed r and n with 1≤r≤n, n≥2, X_0,n=0, characterizes the exponential distribution. Under the assumption of monotone hazard rate the conjecture of Kakosyan, Klebanov and Melamed follows from the above result with r=1.     

Characterization of Lindley distribution by truncated moments

In the past few years, the Lindley distribution has gained popularity for modeling lifetime data as an alternative to the exponential distribution. This paper provides two new characterizations of the Lindley distribution. The first characterization is based on a relation between left truncated moments and failure rate function. The second characterization is based on a relation between right truncated moments and reversed failure rate function.     

Record values and the geometric distribution

Suppose {X_n, n≥1} is a sequence of independent and identically distributed discrete random variables having the common distribution function F(x). The exact distribution of the n-th record value is given under the assumption that F(x) has the geometric distribution. Various properties of the record values and some new characterizations of the geometric distribution are presented.     

Record values of exponentially distributed random variables

A sequence {X_n, n≥1} of independent and identically distributed random variables with absolutely continuous (with respect to Lebesque measure) cumulative distribution function F(x) is considered. X_j is a record value of this sequence if X_j>max(X₁,…,X_j?1), j>1. Let {X_L(n), n≥0} with L(o)=1 be the sequence of such record values and Z_n,n?1=X_L(n)–X_L(n?1). Some properties of Z_n,n?1 are studied and characterizations of the exponential distribution are discussed in terms of the expectation and the hazard rate of z_n,n?1.     

On characterization of the exponential distribution by spacings

Let X be a non-negative random variable with cumulative probability distribution function F. Suppse X₁, X₂, ..., X_n be a random sample of size n from F and X_i,n is the i-th smallest order statistics. We define the standardized spacings D_r,n=(n-r) (X_r+1,n-X_r,n), 1≤r≤n, with D_O,n=nX_1,n and D_n,n=0. Characterizations of the exponential distribution are given by considering the expectation and hazard rates of D_r,n.     

Estimation of parameters of a pareto distribution by generalized order statistics

In this paper we address the problem of estimating the parameters of Pareto II distribution based on generalized order statistics. The estimators based on order statistics and record values are shown to be special cases of these estimators.     

Characterizations of Student's t-distribution via regressions of order statistics

Utilizing regression properties of order statistics, we characterize a family of distributions introduced by Akhundov et al. [New characterizations by properties of midrange and related statistics, Commun. Stat. Theory Methods 33(12) (2004), pp. 3133–3143], which includes the t-distribution with two degrees of freedom as one of its members. Then we extend this characterization result to t-distribution with more than two degrees of freedom.     

Recurrence relations for single and product moments of record values from generalized pareto distribution

In this paper we establish some recurrence relations satisfied by single and product moments of upper record values from the generalized Pareto distribution. It is shown that these relations may be used to obtain all the single and product moments of all record values in a simple recursive manner. We also show that similar results established recently by Balakrishnan and Ahsanullah (1993) for the upper record values from the exponential distribution may be deduced by letting the shape parameter p tend to 0.     

A new extension of the Fréchet distribution: Properties and its characterization

A new lifetime model, which extends the Fréchet distribution called the generalized transmuted Fréchet distribution is proposed and studied. Various of its structural properties including ordinary and incomplete moments, generating function, residual and reversed residual lifes, order statistics and probability weighted moments are derived. Two characterization theorems are presented. The maximum likelihood method is used to estimate the model parameters. The flexibility of the new distribution is illustrated using a real data set. It can serve as an alternative model to other lifetime models available in the literature for modeling positive real data in many areas.