A wrong advice concerning the test F Snedecor

2016 ◽  
Vol 61 (3) ◽  
pp. 61-67
Author(s):  
Antoni Drapella
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Critical Value ◽  
Cumulative Distribution ◽  
Test Scheme ◽  
Test Statistics ◽  
Monte Carlo Experiments ◽  
F Distribution ◽  
Sample Variances

Readers of some domestic statistical textbooks and Internet publications related to F test are advised to accomplish the following test scheme: After having sample variances calculated use quotient of greater to smaller of them as the test statistics. Then take 1 quantile of the F distribution as the critical value. This paper identifies this advice to be wrong and gives reason for it: test statistics in question definitely does not follow the F distribution. So, derivation of the proper test statistics named WF as well as the method of calculating WF' s cumulative distribution function is given. Analytical considerations are confirmed by two Monte Carlo experiments. These show that following the advice one makes first type error two times greater than wanted.

Saddlepoint approximations for bivariate distributions

1990 ◽  
Vol 27 (03) ◽  
pp. 586-597 ◽  
Author(s):  
Suojin Wang
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Normal Distribution ◽  
Cumulative Distribution Function ◽  
Saddlepoint Approximation ◽  
Monte Carlo Study ◽  
Cumulative Distribution ◽  
Normal Distribution Function ◽  
Sample Mean ◽  
Saddlepoint Approximations

A saddlepoint approximation is derived for the cumulative distribution function of the sample mean of n independent bivariate random vectors. The derivations use Lugannani and Rice's saddlepoint formula and the standard bivariated normal distribution function. The separate versions of the approximation for the discrete cases are also given. A Monte Carlo study shows that the new approximation is very accurate.

Saddlepoint approximations for bivariate distributions

1990 ◽  
Vol 27 (3) ◽  
pp. 586-597 ◽  
Author(s):  
Suojin Wang
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Normal Distribution ◽  
Cumulative Distribution Function ◽  
Saddlepoint Approximation ◽  
Monte Carlo Study ◽  
Cumulative Distribution ◽  
Normal Distribution Function ◽  
Sample Mean ◽  
Saddlepoint Approximations

A saddlepoint approximation is derived for the cumulative distribution function of the sample mean of n independent bivariate random vectors. The derivations use Lugannani and Rice's saddlepoint formula and the standard bivariated normal distribution function. The separate versions of the approximation for the discrete cases are also given. A Monte Carlo study shows that the new approximation is very accurate.

scholarly journals Moments of Distance from a Vertex to a Uniformly Distributed Random Point within Arbitrary Triangles

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Hongjun Li ◽  
Xing Qiu
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Standard Deviation ◽  
Probability Density Function ◽  
Monte Carlo Simulations ◽  
Cumulative Distribution Function ◽  
Random Point ◽  
Cumulative Distribution ◽  
Computational Technique ◽  
Probability Density Function Pdf

We study the cumulative distribution function (CDF), probability density function (PDF), and moments of distance between a given vertex and a uniformly distributed random point within a triangle in this work. Based on a computational technique that helps us provide unified formulae of the CDF and PDF for this random distance then we compute its moments of arbitrary orders, based on which the variance and standard deviation can be easily derived. We conduct Monte Carlo simulations under various conditions to check the validity of our theoretical derivations. Our method can be adapted to study the random distances sampled from arbitrary polygons by decomposing them into triangles.

DISSONANCE — A MEASURE OF VARIABILITY FOR ORDINAL RANDOM VARIABLES

2001 ◽  
Vol 09 (01) ◽  
pp. 39-53 ◽  
Author(s):  
RONALD R. YAGER
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Random Variables ◽  
Cumulative Distribution ◽  
General Properties

We look at the issue of obtaining a variance like measure associated with probability distributions over ordinal sets. We call these dissonance measures. We specify some general properties desired in these dissonance measures. The centrality of the cumulative distribution function in formulating the concept of dissonance is pointed out. We introduce some specific examples of measures of dissonance.

Estimating the cumulative distribution function for the linear combination of gamma random variables

2017 ◽  
Vol 20 (5) ◽  
pp. 939-951
Author(s):  
Amal Almarwani ◽  
Bashair Aljohani ◽  
Rasha Almutairi ◽  
Nada Albalawi ◽  
Alya O. Al Mutairi
Keyword(s):  
Distribution Function ◽  
Linear Combination ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Cumulative Distribution
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