scholarly journals Evaluation of a Multiple Integral of Tefera via Properties of the Exponential Distribution

10.37236/904 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Yaming Yu
Keyword(s):  
Exponential Distribution ◽  
Multiple Integral ◽  
Combinatorial Identities ◽  
Integral Evaluation ◽  
Basic Probability ◽  
Wz Method

An interesting integral originally obtained by Tefera ("A multiple integral evaluation inspired by the multi-WZ method," Electron. J. Combin., 1999, #N2) via the WZ method is proved using calculus and basic probability. General recursions for a class of such integrals are derived and associated combinatorial identities are mentioned.

scholarly journals A Multiple Integral Evaluation Inspired by the Multi-WZ Method

10.37236/1478 ◽  
1999 ◽  
Vol 6 (1) ◽  
Author(s):  
Akalu Tefera
Keyword(s):  
Integral Identity ◽  
Multiple Integral ◽  
Continuous Version ◽  
Integral Evaluation ◽  
Wz Method

We give an integral identity which was conjectured and proved by using the continuous version of the multi-WZ method.

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.

Application of flow systems in laboratory diagnostics for the integral evaluation of the hemostatic system

2018 ◽  
Vol 17 (1) ◽  
pp. 117-129
Author(s):  
O.E. Ushakova ◽  
◽  
D.Y. Nechipurenko ◽  
A.A. Butylin ◽  
M.A. Panteleev ◽  
...  
Keyword(s):  
Laboratory Diagnostics ◽  
Integral Evaluation ◽  
Hemostatic System ◽  
Flow Systems

The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

2018 ◽  
pp. 439
Author(s):  
Hazim Mansour Gorgees ◽  
Bushra Abdualrasool Ali ◽  
Raghad Ibrahim Kathum
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Reliability Function ◽  
Bayes Estimator ◽  
Likelihood Estimator ◽  
Monte Carlo Simulation Technique ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Better Than

     In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable

2020 ◽  
Vol 17 (2) ◽  
pp. 256-277
Author(s):  
Ol'ga Veselovska ◽  
Veronika Dostoina
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Analytic Functions ◽  
Combinatorial Identities ◽  
Independent Interest ◽  
Closed Curves ◽  
In Series ◽  
Derivatives Of

For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

Probability

2017 ◽  
Author(s):  
Andrew Gelman ◽  
Deborah Nolan
Keyword(s):  
Conditional Probability ◽  
Bayes Rule ◽  
Probability Models ◽  
Classroom Activities ◽  
Basic Probability

This chapter contains many classroom activities and demonstrations to help students understand basic probability calculations, including conditional probability and Bayes rule. Many of the activities alert students to misconceptions about randomness. They create dramatic settings where the instructor discerns real coin flips from fake ones, students modify dice and coins in order to load them, students “accused” of lying based on the outcome of an inaccurate simulated lie detector face their classmates. Additionally, probability models of real outcomes offer good value: first we can do the probability calculations, and then can go back and discuss the potential flaws of the model.

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