1
1726-4057
Iranian Statistical Society
219
60: Probability theory and stochastic processes
Ordered Random Variables from Discontinuous Distributions
Balakrishnan
N.
Dembin ́ska
A.
1
3
2007
6
1
0
0
21
08
2013
12
09
2015
In the absolutely continuous case, order statistics, record values and several other models of ordered random variables can be viewed as special cases of generalized order statistics, which enables a unified treatment of their theory. This paper deals with discontinuous generalized order statistics, continuing on the recent work of Tran (2006). Specifically, we show that in general neither records nor weak records are submodels of discrete generalized order statistics. Next, we show that progressively Type-II right censored order statistics from an arbitrary distribution can be embedded in the model of generalized order statistics and then use this fact to establish some distributional properties of progressively Type-II right censored order statistics. Finally, we present some characterizations of the geometric distribution based on progressively Type-II right censored order statistics.
217
60: Probability theory and stochastic processes
Outer and Inner Confidence Intervals Based on Extreme Order Statistics in a Proportional Hazard Model
Ahmadi
J.
Razmkhah
M.
1
3
2007
6
1
1
16
21
08
2013
12
09
2015
Let Mi and Mi be the maximum and minimum of the ith sample from k independent sample with different sample sizes, respectively. Suppose that the survival distribution function of the ith sample is F ̄i = F ̄αi, where αi is known and positive constant.
It is shown that how various exact non-parametric inferential proce-
′
dures can be developed on the basis of Mi’s and Mi ’s for distribution function F without any assumptions about it other than F is continuous. These include outer and inner confidence intervals for quantile intervals and upper and lower confidence limits for quantile differences. Three schemes have been investigated and in each case, the associated confidence coefficients are obtained. A numerical example is given in order to illustrate the proposed procedure.
218
60: Probability theory and stochastic processes
Bayesian Prediction Intervals for Future Order Statistics from the Generalized Exponential Distribution
A. Alamm
Ahmad
Raqab
Mohammad Z.
Madi
Mohamed T.
1
3
2007
6
1
17
30
21
08
2013
12
09
2015
Let X1, X2, ..., Xr be the first r order statistics from a sample of size n from the generalized exponential distribution with shape parameter θ. In this paper, we consider a Bayesian approach to predicting future order statistics based on the observed ordered data. The predictive densities are obtained and used to determine prediction intervals for unobserved order statistics for one-sample and two-sample prediction plans. A numerical study is conducted to il- lustrate the prediction procedures.
220
60: Probability theory and stochastic processes
On the Distribution and Moments of Record Values in Increasing Populations
Charalambides
Ch. A.
1
3
2007
6
1
47
60
21
08
2013
12
09
2015
Consider a sequence of n independent observations from a population of increasing size αi, i = 1,2,... and an absolutely continuous initial distribution function. The distribution of the kth record value is represented as a countable mixture, with mixing the distribution of the kth record time and mixed the distribution of the nth order statistic. Precisely, the distribution function and (power) moments of the kth record value are expressed by series, with co- efficients being the signless generalized Stirling numbers of the first kind. Then, the probability density function and moments of the kth record value in a geometrically increasing population are expressed by q-series, with coefficients being the signless q-Stirling numbers of the first kind. In the case of a uniform distribution for the initial popu- lation, two equivalent q-series expressions of the jth (power) moment of the kth record value are derived. Also, the distribution function and the moments of the kth record value in a factorially increasing population are deduced.
221
60: Probability theory and stochastic processes
Multivariate Dispersive Ordering of Generalized Order Statistics
Chen
Jing
Hu
Taizhong
1
3
2007
6
1
61
75
21
08
2013
12
09
2015
The concept of generalized order statistics (GOSs) was introduced as a unified approach to a variety of models of ordered random variables. The purpose of this paper is to investigate condi- tions on the underlying distribution functions and the parameters on which GOSs are based, to establish Shaked-Shanthikumar multivari- ate dispersive ordering of GOSs from one sample and Khaledi-Kochar multivariate dispersive ordering of GOSs from two samples. Some ap- plications are also given.
222
60: Probability theory and stochastic processes
Testing Exponentiality Based on Record Values
Habibi Rad
A.
Yousefzadeh
F.
Amini
M.
Arghami
N. R.
1
3
2007
6
1
77
87
21
08
2013
12
09
2015
We introduce a goodness of fit test for exponentiality based on record values. The critical points and powers for some alternatives are obtained by simulation.