Estimates of Characteristic Functions of Some Random Variables with Applications to $\omega ^2 $-Statistics. II

1986 ◽  
Vol 30 (1) ◽  
pp. 117-127 ◽  
Author(s):  
Yu. V. Borovskikh
Keyword(s):  
Random Variables ◽  
Characteristic Functions

On the Distribution of Sum of Independent Positive Binomial Variables

1970 ◽  
Vol 13 (1) ◽  
pp. 151-152 ◽  
Author(s):  
J. C. Ahuja
Keyword(s):  
Power Series ◽  
Inversion Formula ◽  
Probability Function ◽  
Random Variables ◽  
Random Variable ◽  
Characteristic Functions ◽  
Binomial Probability ◽  
Generalized Power Series ◽  
Alternative Derivation ◽  
Image Position

Let X1, X2, …, Xn be n independent and identically distributed random variables having the positive binomial probability function1where 0 < p < 1, and T = {1, 2, …, N}. Define their sum as Y=X1 + X2 + … +Xn. The distribution of the random variable Y has been obtained by Malik [2] using the inversion formula for characteristic functions. It appears that his result needs some correction. The purpose of this note is to give an alternative derivation of the distribution of Y by applying one of the results, established by Patil [3], for the generalized power series distribution.

Analytic solution of a finite dam governed by a general input

1974 ◽  
Vol 11 (01) ◽  
pp. 134-144 ◽  
Author(s):  
S. K. Srinivasan
Keyword(s):  
Total Duration ◽  
Random Variables ◽  
Rational Functions ◽  
Characteristic Functions ◽  
Dry Period ◽  
Laplace Transform Technique ◽  
Independent Families ◽  
Set Up ◽  
Input Form ◽  
Finite Dam

A stochastic model of a finite dam in which the epochs of input form a renewal process is considered. It is assumed that the quantities of input at different epochs and the inter-input times are two independent families of random variables whose characteristic functions are rational functions. The release rate is equal to unity. An imbedding equation is set up for the probability frequency governing the water level in the first wet period and the resulting equation is solved by Laplace transform technique. Explicit expressions relating to the moments of the random variables representing the number of occasions in which the dam becomes empty as well as the total duration of the dry period in any arbitrary interval of time are indicated for negative exponentially distributed inter-input times.

Some joint distributions in Bernoulli excursions

1994 ◽  
Vol 31 (A) ◽  
pp. 239-250
Author(s):  
Endre Csáki
Keyword(s):  
Random Walk ◽  
Random Variables ◽  
Characteristic Functions ◽  
Symmetric Random Walk ◽  
Joint Distributions ◽  
Recursion Formulas

Some exact and asymptotic joint distributions are given for certain random variables defined on the excursions of a simple symmetric random walk. We derive appropriate recursion formulas and apply them to get certain expressions for the joint generating or characteristic functions of the random variables.

Large correlated families of positive random variables

1988 ◽  
Vol 103 (1) ◽  
pp. 147-162 ◽  
Author(s):  
D. H. Fremlin
Keyword(s):  
Probability Space ◽  
Random Variables ◽  
Characteristic Functions ◽  
Measurable Functions ◽  
Uniformly Bounded

S. Argyros and N. Kalamidas([l], repeated in [2], Theorem 6·15) proved the following. If κ is a cardinal of uncountable cofinality, and 〈Eξ〉ξ<κ is a family of measurable sets in a probability space (X, μ) such that infξ<κμEξ = δ, and if n ≥ 1, , then there is a set Γ ⊆ κ such that #(Γ) = κ and μ(∩ξ∈IEξ) ≥ γ whenever I ⊆ ξ has n members. In Proposition 7 below I refine this result by (i) taking any γ < δn (which is best possible) and (ii) extending the result to infinite cardinals of countable cofinality, thereby removing what turns out to be an irrelevant restriction. The proof makes it natural to perform a further extension to general uniformly bounded families of non-negative measurable functions in place of characteristic functions.

Remarks on the relation between fractional moments and fractional derivatives of characteristic functions

1980 ◽  
Vol 17 (02) ◽  
pp. 456-466 ◽  
Author(s):  
G. Laue
Keyword(s):  
Fractional Derivatives ◽  
Random Variables ◽  
Characteristic Functions ◽  
Fractional Moments ◽  
Derivatives Of

We consider fractional derivatives of characteristic functions. We use these fractional derivatives for the formulation of new conditions for the existence of non-integer moments. We also compare the known conditions for the existence of moments of arbitrary random variables with our new conditions. As a consequence many conditions can be written in a unified terminology.

scholarly journals Characteristic functions of random variables attracted to $1$-stable laws

1998 ◽  
Vol 26 (1) ◽  
pp. 399-415 ◽  
Author(s):  
Jon Aaronson ◽  
Manfred Denker
Keyword(s):  
Random Variables ◽  
Stable Laws ◽  
Characteristic Functions
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