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Full-Text Articles in Statistical Models
Are Highly Dispersed Variables More Extreme? The Case Of Distributions With Compact Support, Benedict E. Adjogah
Are Highly Dispersed Variables More Extreme? The Case Of Distributions With Compact Support, Benedict E. Adjogah
Electronic Theses and Dissertations
We consider discrete and continuous symmetric random variables X taking values in [0; 1], and thus having expected value 1/2. The main thrust of this investigation is to study the correlation between the variance, Var(X) of X and the value of the expected maximum E(Mn) = E(X1,...,Xn) of n independent and identically distributed random variables X1,X2,...,Xn, each distributed as X. Many special cases are studied, some leading to very interesting alternating sums, and some progress is made towards a general theory.
Some New Probability Distributions Based On Random Extrema And Permutation Patterns, Jie Hao
Some New Probability Distributions Based On Random Extrema And Permutation Patterns, Jie Hao
Electronic Theses and Dissertations
In this paper, we study a new family of random variables, that arise as the distribution of extrema of a random number N of independent and identically distributed random variables X1,X2, ..., XN, where each Xi has a common continuous distribution with support on [0,1]. The general scheme is first outlined, and SUG and CSUG models are introduced in detail where Xi is distributed as U[0,1]. Some features of the proposed distributions can be studied via its mean, variance, moments and moment-generating function. Moreover, we make some other choices for …