Jagdish Saran

On the distribution of crossings in a generalized random walk

Abstract This paper deals with the derivation of the probability distribution of the rank order statistic N ∗ μ, n ( r ), the number of crossings of height r (≥0) in a generalized random walk with steps 1 and −μ by using the modified Dwass technique.

On the fluctuations of partial sums

For non-negative integral valued interchangeable random variables Takacs [6, 7] has derived the probability distributions of certain statistics viz. concerning the partial sums . This paper deals with the probability distributions of some other statistics viz. concerning the partial sums , of geometric random variables . These distributions have been derived by employing the random walk model as used by Cs´ki-Vincze [1], Sen [4, 5] and Saran [3].

Rank Order Statistics Related to a Generalized Random Walk

This paper deals with the derivation of the joint and marginal distributions of certain rank order statistics related to the generalized random walk with steps +1 and −µ by using the extended Dwass technique evolved by Mohanty and Handa (1970). These generalize and extend the results of Saran and Rani (1991a, b).

On Joint Distuibutions Of Rank Order Statisties for Equal Sample Sizes

This paper deals with the two–sample (equal sized)problem where Fa(x)and Ga(x)are the two empirical distribution functions and investigates the null joint and marginal distributions of certain rank order statistics through the technique of DWASS(1967 based on simple random walk with indipendent steps,thus generalizing and unifying the results of DWASS(1967),ANEJA (1975)and MAHENDRA PRATAP(1982)

The Kumaraswamy-Burr III Distribution Based on Upper Record Values

SYNOPTIC ABSTRACT This article addresses the problem of frequent estimation of the parameters of the Kumaraswamy-Burr III distribution using upper record values. The explicit expressions and recurrence relations satisfied by the single and product moments of kth upper record values from Kumaraswamy-Burr III distribution are also derived. The corresponding results for upper record values are obtained as special cases. Further, using a recurrence relation for single moments and conditional expectation of record values, we obtain characterization of this distribution. The method of maximum likelihood is adopted for estimating the model parameters. For different parameter settings and sample sizes, various simulation studies have been performed and their performances are compared. Finally, a real data example is discussed to illustrate its applicability.

Bonferroni and Gini Indices and Recurrence Relations for Moments of Progressive Type-II Right Censored Order Statistics from Marshall-Olkin Exponential Distribution

In this paper, we derive explicit expressions for Bonferroni Curve (BC), Bonferroni index (BI), Lorenz Curve (LC) and Gini index (GI) for the Marshall-Olikn Exponential (MOE) distribution, which have mainly concern with some aspects like poverty, welfare, decomposability, reliability, sampling and inference. We also establish several recurrence relations satisfied by the single and the product moments of progressive Type-II right censored order statistics from MOE distribution, to enable one to evaluate the single and product moments of all order in a simple recursive way.

Joint distributions based on the number of runs and some other two-sample rank order statistics for arbitrary sample sizes

Abstract This paper is concerned with the derivation of the joint and marginal distributions of some rank order statistics associated with the two-sample problem for samples of arbitrary sizes m, n (m ≠ n) under the null hypothesis of equality of distributions assumed otherwise to be continuous. The rank order statistics considered include the following quantities in the random walk: the number of crossings of height t, the number of visits at height t, the number of visits at height t from above (where t ≥ 0), and the number of runs up and down.

On the distributions of D+ mn , R+ mn (j) And Q+ mn

This paper deals with the two-sample problem and investigates the joint and marginal distributions of D+ mn the Smirnov one-sided statistic, R+ mn (j), the index where D+ mn is achieved for the jth time (j≤1) and Q+ mn , the number of times D+ mn is achieved.

Distributions based on upcrossings, upward crossings, positive reflections and their runs in a generalized random walk

This paper deals with the derivation of the joint and marginal probability distributions of same rank order statistics related to the generalized random walk with steps +1 and -μ by using the extended Dwass technique evolved by Mohanty and Handa (1970). The rank order statistics considered include number of upcrossings, number of upward crossings, number of positive reflections and their runs.

Generalized random walk and distributions of some rank order statistics

Abstract This paper deals with the derivation of the joint and marginal probability distributions of some rank order statistics related to the generalized random walk with steps 1 and -μ by using the extended Dwass technique. The rank order statistics considered include total length of all sojourns above height r, number of crossings of height r, number of sojourns at height r and the number of sojourns at height r from above (r>0).