The Approximation of Sum of Independent Distributions by the Erlang Distribution Function

2002 ◽  
Vol 7 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Antanas Karoblis
Keyword(s):  
Distribution Function ◽  
Exponential Distribution ◽  
Queueing Theory ◽  
Erlang Distribution ◽  
Estimation Of Error

The exponential distribution and the Erlang distribution function are been used in numerous areas of mathematics, and specifically in the queueing theory. Such and similar applications emphasize the importance of estimation of error of approximation by the Erlang distribution function. The article gives an analysis and technique of error’s estimation of an accuracy of such approximation, especially in some specific cases.

STOCHASTIC TRANSMISSION DYNAMICS OF COVID-19 WITHIN A DENSITY DEPENDENT POPULATION

10.33003/659 ◽  
2021 ◽  
Vol 5 (2) ◽  
pp. 567-573
Author(s):  
Lubem M. Kwaghkor ◽  
Stephen E. Onah ◽  
Ibrahim G. Basi ◽  
Theophilus Danjuma
Keyword(s):  
Distribution Function ◽  
Exponential Distribution ◽  
Severe Disease ◽  
The Elderly ◽  
Control Measures ◽  
Special Treatment ◽  
Susceptible Population ◽  
Density Dependent ◽  
Infected People ◽  
Population Sizes

Coronavirus diseases (COVID-19) is a respiratory disease. Most infected people are known to develop mild to moderate symptoms and recover without requiring special treatment except for those who have underlying medical conditions and the elderly have a higher risk of developing severe disease. This research is aimed at studying the probable spread of the COVID-19 virus within a completely susceptible density-dependent population using a modified exponential distribution function. The modified exponential distribution function was extended to include the Basic Reproduction Number which was computed using the Nigerian COVID-19 index cases from 27th February to 18th April, 2020 to be. Various interesting results were obtained for the including the time period for the spread for different population sizes. The duration of the spread of the virus is from 4 to 7 hours with an average of 5.5 hours. This indicates that, for one infectious person with  to enter a completely susceptible population of size , the virus can spread through the entire population in about  hours if no control measures are in place.

Characterizations of the exponential distribution by order statistics

1974 ◽  
Vol 11 (03) ◽  
pp. 605-608 ◽  
Author(s):  
J. S. Huang
Keyword(s):  
Distribution Function ◽  
Order Statistics ◽  
Exponential Distribution ◽  
Special Cases ◽  
Characterization Theorems

Let X 1,n ≦ … ≦ Xn, n be the order statistics of a sample of size n from a distribution function F. Desu (1971) showed that if for all n ≧ 2, nX 1,n is identically distributed as X 1, 1, then F is the exponential distribution (or else F degenerates). The purpose of this note is to point out that special cases of known characterization theorems already constitute an improvement over this result. We show that the characterization is preserved if “identically distributed” is weakened to “having identical (finite) expectation”, and “for all n ≧ 2” is weakened to “for a sequence of n's with divergent sum of reciprocals”.

scholarly journals The Characteristic Function Property of Mixture Negative Binomial-Exponential Distribution

2018 ◽  
Vol 3 (4) ◽  
pp. 178
Author(s):  
Dodi Devianto ◽  
Sarah Sarah ◽  
Siska Dwi Kumala ◽  
Maiyastri Maiyastri
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Characteristic Function ◽  
Exponential Distribution ◽  
Negative Binomial Distribution ◽  
Probability Distribution Function ◽  
Negative Binomial ◽  
Stieltjes Transform ◽  
Function Property ◽  
New Distribution

This paper introduces a new distribution by mixing the negative binomial distribution and exponential distribution namely negative binomial-exponential (NB-E) distribution. In is given the probability distribution function of NB-E distribution and its characteristic function by using Fourier-Stieltjes transform. In addition we present the some properties of characteristic function from NB-E distribution.

A heavy traffic result for the finite dam

1973 ◽  
Vol 10 (01) ◽  
pp. 223-228 ◽  
Author(s):  
Nils Blomqvist
Keyword(s):  
Steady State ◽  
Exponential Distribution ◽  
Discrete Time ◽  
Queueing Theory ◽  
Heavy Traffic ◽  
Previous Knowledge ◽  
Finite Dam ◽  
State Content ◽  
General Conditions

The steady state content Z of a finite dam in discrete time is investigated for small absolute values of the expected net input and correspondingly large values of the dam capacity. It is shown that under general conditions Z has, asymptotically, a truncated exponential distribution, a result that supplements previous knowledge in queueing theory.

Random arcs on the circle

1978 ◽  
Vol 15 (04) ◽  
pp. 774-789 ◽  
Author(s):  
Andrew F. Siegel
Keyword(s):  
Integral Equation ◽  
Distribution Function ◽  
Exponential Distribution ◽  
Asymptotic Distribution ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution

Place n arcs of equal lengths randomly on the circumference of a circle, and let C denote the proportion covered. The moments of C (moments of coverage) are found by solving a recursive integral equation, and a formula is derived for the cumulative distribution function. The asymptotic distribution of C for large n is explored, and is shown to be related to the exponential distribution.

Recursive estimation of distributional fix-points

2000 ◽  
Vol 37 (01) ◽  
pp. 73-87
Author(s):  
Paul Embrechts ◽  
Harro Walk
Keyword(s):  
Stochastic Process ◽  
Distribution Function ◽  
Stochastic Approximation ◽  
Stochastic Models ◽  
Queueing Theory ◽  
Renewal Theory ◽  
Random Variable ◽  
Recursive Estimation ◽  
Real Random Variable ◽  
Index Space

In various stochastic models the random equation of implicit renewal theory appears where the real random variable S and the stochastic process Ψ with index space and state space R are independent. By use of stochastic approximation the distribution function of S is recursively estimated on the basis of independent or ergodic copies of Ψ. Under integrability assumptions almost sure L 1-convergence is proved. The choice of gains in the recursion is discussed. Applications are given to insurance mathematics (perpetuities) and queueing theory (stationary waiting and queueing times).

Approximating a Cumulative Distribution Function by Generalized Hyperexponential Distributions

1997 ◽  
Vol 11 (1) ◽  
pp. 11-18 ◽  
Author(s):  
Jihong Ou ◽  
Jingwen Li ◽  
Süleyman Özekici
Keyword(s):  
Distribution Function ◽  
Performance Measures ◽  
Stochastic Models ◽  
Queueing Theory ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Idle Period ◽  
Period Distribution ◽  
Different Types ◽  
Recent Developments

Recent developments in stochastic modeling show that enormous analytical advantages can be gained if a general cumulative distribution function (c.d.f.) can be approximated by generalized hyperexponential distributions. In this paper, we introduce a procedure to explicitly construct such approximations of an arbitrary c.d.f. Although our approach can be used in different types of stochastic models, the main motivation comes from queueing theory in obtaining approximations of the idle-period distribution and other performance measures in GI/G/1 queues.

scholarly journals The uncertainty measure for q-exponential distribution function

2013 ◽  
Vol 58 (13) ◽  
pp. 1524-1528 ◽  
Author(s):  
CongJie Ou ◽  
Aziz El Kaabouchi ◽  
QiuPing Alexandre Wang ◽  
JinCan Chen
Keyword(s):  
Distribution Function ◽  
Exponential Distribution ◽  
Uncertainty Measure

scholarly journals ON EXTREME VALUES OF BIRTH AND DEATH PROCESSES

2021 ◽  
Vol 9 (1) ◽  
pp. 237-249
Author(s):  
I. Matsak
Keyword(s):  
Limit Theorem ◽  
Convergence Rate ◽  
Exponential Distribution ◽  
Queueing Theory ◽  
Extreme Values ◽  
Birth And Death Processes ◽  
Uniform Estimates ◽  
Regeneration Cycle ◽  
The Right ◽  
Right Order

We establish the convergence rate to exponential distribution in a limit theorem for extreme values of birth and death processes. Some applications of this result are given to processes specifying queue length.). We establish uniform estimates for the convergence rate in the exponential distribution in a limit theorem for extreme values of birth and death processes. This topic is closely related to the problem on the time of first intersection of some level u by a regenerating process. Of course, we assume that both time t and level u grow infinitely. The proof of our main result is based on an important estimate for general regenerating processes. Investigations of the kind are needed in different fields: mathematical theory of reliability, queueing theory, some statistical problems in physics. We also provide with examples of applications of our results to extremal queueing problems M/M/s. In particular case of queueing M/M/1, we show that the obtained estimates have the right order with respect to the probability q(u) of the exceeding of a level u at one regeneration cycle, that is, only improvement of the corresponding constants is possible.

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