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.

Saddlepoint approximations in conditional inference

1993 ◽  
Vol 30 (2) ◽  
pp. 397-404 ◽  
Author(s):  
Suojin Wang
Keyword(s):  
Distribution Function ◽  
Linear Function ◽  
Relative Error ◽  
Cumulative Distribution Function ◽  
Conditional Inference ◽  
Cumulative Distribution ◽  
Important Work ◽  
Sample Mean ◽  
Saddlepoint Approximations ◽  
Higher Dimensional

Saddlepoint approximations are derived for the conditional cumulative distribution function and density of where is the sample mean of n i.i.d. bivariate random variables and g(x, y) is a non-linear function. The relative error of order O(n–1) is retained. The results extend the important work of Skovgaard (1987), and are useful in conditional inference, especially in the case of small or moderate sample sizes. Generalizations to higher-dimensional random vectors are also discussed. Some examples are demonstrated.

Saddlepoint approximations in conditional inference

1993 ◽  
Vol 30 (02) ◽  
pp. 397-404
Author(s):  
Suojin Wang
Keyword(s):  
Distribution Function ◽  
Linear Function ◽  
Relative Error ◽  
Cumulative Distribution Function ◽  
Conditional Inference ◽  
Cumulative Distribution ◽  
Important Work ◽  
Sample Mean ◽  
Saddlepoint Approximations ◽  
Higher Dimensional

Saddlepoint approximations are derived for the conditional cumulative distribution function and density of where is the sample mean of n i.i.d. bivariate random variables and g(x, y) is a non-linear function. The relative error of order O(n –1) is retained. The results extend the important work of Skovgaard (1987), and are useful in conditional inference, especially in the case of small or moderate sample sizes. Generalizations to higher-dimensional random vectors are also discussed. Some examples are demonstrated.

Asymptotic Approximation of an Integral Involving the Normal Distribution*

1986 ◽  
Vol 29 (2) ◽  
pp. 167-176 ◽  
Author(s):  
J. P. McClure ◽  
R. Wong
Keyword(s):  
Distribution Function ◽  
Normal Distribution ◽  
Positive Constant ◽  
Asymptotic Approximation ◽  
Cumulative Distribution Function ◽  
Random Variable ◽  
Normal Random Variable ◽  
Cumulative Distribution ◽  
Standard Normal Random Variable ◽  
Standard Normal

AbstractAn asymptotic approximation is obtained, as k → ∞, for the integralwhere Φ is the cumulative distribution function for a standard normal random variable, and L is a positive constant. The problem is motivated by a question in statistics, and an outline of'the application is given. Similar methods may be used to approximate other integrals involving the normal distribution.

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.

ON THE GENERALISATION OF SIDEL’NIKOV’S THEOREM TO -ARY LINEAR CODES

2019 ◽  
Vol 101 (1) ◽  
pp. 157-162
Author(s):  
YILUN WEI ◽  
BO WU ◽  
QIJIN WANG
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Linear Codes ◽  
Cumulative Distribution ◽  
Standard Normal Distribution ◽  
Binary Codes ◽  
Normal Distribution Function ◽  
Code Length ◽  
Standard Normal Distribution Function ◽  
Standard Normal

We generalise Sidel’nikov’s theorem from binary codes to $q$-ary codes for $q>2$. Denoting by $A(z)$ the cumulative distribution function attached to the weight distribution of the code and by $\unicode[STIX]{x1D6F7}(z)$ the standard normal distribution function, we show that $|A(z)-\unicode[STIX]{x1D6F7}(z)|$ is bounded above by a term which tends to $0$ when the code length tends to infinity.

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.

Sign in / Sign up

Export Citation Format

Share Document