Limit Laws for Cumulative Sums of Independent Random Variables with a Finite Number of Distribution Types

1971 ◽  
Vol 16 (4) ◽  
pp. 596-619 ◽  
Author(s):  
A. A. Zinger
Keyword(s):  
Finite Number ◽  
Random Variables ◽  
Independent Random Variables ◽  
Limit Laws ◽  
Cumulative Sums

On the Sequential Detection Problem

1989 ◽  
Vol 38 (3-4) ◽  
pp. 129-146
Author(s):  
Uttam Bandyopadhyay
Keyword(s):  
Infinite Sequence ◽  
Random Variables ◽  
Stopping Rule ◽  
Independent Random Variables ◽  
Sequential Detection ◽  
Detection Problem ◽  
Asymptotic Results ◽  
Rule Based ◽  
Unknown Point ◽  
Cumulative Sums

In this paper, for an infinite sequence of independent random variables, we have considered the problem of estimation of an unknown point ( q) where a change in the distribution of the random variables occurs. Attaching suitable scores for the observed values. of the random variables, a stopping rule based on the cumulative sums of these scores has been proposed. Some asymptotic results useful for studying the performance of the proposed procedure havo beon obtained.

scholarly journals Limit laws for products of free and independent random variables

2000 ◽  
Vol 141 (1) ◽  
pp. 43-52 ◽  
Author(s):  
Hari Bercovici ◽  
Vittorino Pata
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Limit Laws

Limit Laws for Power Normalized Partial Maxima of Independent Random Variables Having one of m Specified Distributions

2000 ◽  
Vol 50 (1-2) ◽  
pp. 1-16 ◽  
Author(s):  
S. Ravi
Keyword(s):  
Asymptotic Behaviour ◽  
Random Variables ◽  
Distribution Functions ◽  
Subject Classification ◽  
Independent Random Variables ◽  
Limit Laws ◽  
Primary 60F99 ◽  
Independent Observations ◽  
Secondary 60E99

Suppose [Formula: see text] are independent observations from [Formula: see text] distribution functions. In this paper we discuss the asymptotic behaviour of power normalized partial maxima under some assumptions on the distribution functions. AMS (2000} Subject Classification: Primary 60F99; Secondary 60E99.

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Optimal Parameter ◽  
Random Variables ◽  
Kernel Functions ◽  
Independent Random Variables ◽  
Functional Dependencies ◽  
Approximation Properties ◽  
Probability Density Estimation ◽  
Multidimensional Probability ◽  
Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

Methodology of Calculation the Terminal Settling Velocity Distribution of Irregular Particles for High Values of the Reynold’s Number/Metodologia Wyliczania Rozkładu Granicznej Prędkości Opadania Ziaren Nieregularnych Dla Wysokich Wartości Liczb Reynoldsa

2014 ◽  
Vol 59 (2) ◽  
pp. 553-562 ◽  
Author(s):  
Agnieszka Surowiak ◽  
Marian Brożek
Keyword(s):  
Velocity Distribution ◽  
Settling Velocity ◽  
Random Variables ◽  
Independent Random Variables ◽  
Calculation Algorithm ◽  
Shape Coefficient ◽  
Geometrical Properties ◽  
Size And Shape ◽  
Physical Density ◽  
Settling Velocity Distribution

Abstract Settling velocity of particles, which is the main parameter of jig separation, is affected by physical (density) and the geometrical properties (size and shape) of particles. The authors worked out a calculation algorithm of particles settling velocity distribution for irregular particles assuming that the density of particles, their size and shape constitute independent random variables of fixed distributions. Applying theorems of probability, concerning distributions function of random variables, the authors present general formula of probability density function of settling velocity irregular particles for the turbulent motion. The distributions of settling velocity of irregular particles were calculated utilizing industrial sample. The measurements were executed and the histograms of distributions of volume and dynamic shape coefficient, were drawn. The separation accuracy was measured by the change of process imperfection of irregular particles in relation to spherical ones, resulting from the distribution of particles settling velocity.

Ehrenfest urn models

1965 ◽  
Vol 2 (02) ◽  
pp. 352-376 ◽  
Author(s):  
Samuel Karlin ◽  
James McGregor
Keyword(s):  
Exponential Distribution ◽  
Continuous Time ◽  
Random Variables ◽  
Independent Random Variables ◽  
Urn Models ◽  
Time Intervals ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Random Times

In the Ehrenfest model with continuous time one considers two urns and N balls distributed in the urns. The system is said to be in stateiif there areiballs in urn I, N −iballs in urn II. Events occur at random times and the time intervals T between successive events are independent random variables all with the same negative exponential distributionWhen an event occurs a ball is chosen at random (each of theNballs has probability 1/Nto be chosen), removed from its urn, and then placed in urn I with probabilityp, in urn II with probabilityq= 1 −p, (0 <p< 1).

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