scholarly journals Approximation of multivariate distribution functions

2008 ◽  
Vol 58 (5) ◽  
Author(s):  
Margus Pihlak
Keyword(s):  
Distribution Function ◽  
Linear Algebra ◽  
Taylor Expansion ◽  
Simulated Data ◽  
Distribution Functions ◽  
Normal Distribution Function ◽  
Matrix Operation ◽  
Unknown Distribution ◽  
Matrix Integral ◽  
Unknown Distribution Function

AbstractIn the paper the unknown distribution function is approximated with a known distribution function by means of Taylor expansion. For this approximation a new matrix operation — matrix integral — is introduced and studied in [PIHLAK, M.: Matrix integral, Linear Algebra Appl. 388 (2004), 315–325]. The approximation is applied in the bivariate case when the unknown distribution function is approximated with normal distribution function. An example on simulated data is also given.

scholarly journals On the rate of convergence of waiting times

1965 ◽  
Vol 5 (3) ◽  
pp. 365-373 ◽  
Author(s):  
C. K. Cheong ◽  
C. R. Heathcote
Keyword(s):  
Distribution Function ◽  
Rate Of Convergence ◽  
Waiting Times ◽  
Distribution Functions ◽  
Initial Condition ◽  
Hopf Equation ◽  
Unknown Distribution ◽  
Image Position

Let K(y) be a known distribution function on (−∞, ∞) and let {Fn(y), n = 0, 1,…} be a sequence of unknown distribution functions related by subject to the initial condition If the sequence {Fn(y)} converges to a distribution function F(y) then F(y) satisfies the Wiener-Hopf equation

Comparative Study of Probability Distribution Functions of Wind Power Variation

2014 ◽  
Vol 953-954 ◽  
pp. 414-418
Author(s):  
An Jue Dai ◽  
Qian Wang ◽  
Yan Nan Zhou
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Wind Power ◽  
Gaussian Distribution ◽  
Gaussian Mixture ◽  
Second Order ◽  
Distribution Functions ◽  
Normal Distribution Function ◽  
One Dimensional ◽  
Power Variation

This work focuses on the probability distribution function of wind power variation. After analyzing the characters of the power fluctuation data, normal distribution function, t location-scale distribution function and mixed second-order one-dimensional Gaussian distribution function are chosen to describe the wind power variation. Then K-S test(Kolmogorov-Smirnov) test and Pearson product-moment correlation coefficient are used to evaluate the fitting effect of the three distribution functions respectively, which indicates that the mixed second-order one-dimensional Gaussian distribution is the most appropriate one. At last, the factors affecting the parameters of Gaussian mixture distribution and to what degree they can achieve are investigated.

Asymptotical problems of sequential interval and point estimation

2020 ◽  
Vol 86 (7) ◽  
pp. 72-80
Author(s):  
A. A. Abdushukurov ◽  
G. G. Rakhimova
Keyword(s):  
Distribution Function ◽  
Confidence Intervals ◽  
Wide Class ◽  
Sequential Analysis ◽  
Interval Estimation ◽  
Sequential Estimation ◽  
Point Estimation ◽  
Minimum Risk ◽  
Unknown Distribution ◽  
Unknown Distribution Function

The accuracy of interval estimation systems is usually measured using interval lengths for given covering probabilities. The confidence intervals are the intervals of a fixed width if the length of the interval is determined, i.e., not random, and tends to zero for a given covering probability. We consider two important directions of statistical analysis -sequential interval estimation with confidence intervals of fixed width and sequential point estimation with asymptotically minimum risk. Two statistical models are used to describe the basis problems of sequential interval estimation by confidence intervals of a fixed width and point estimation. A review of data on nonparametric sequential estimation is carried out and new original results obtained by the authors are presented. Sequential analysis is characterized by the fact that the moment of termination of observations (stopping time) is random and is determined depending on the values of the observed data and on the adopted measure of optimality of the constructed statistical estimate. Therefore, to solve the asymptotic problems of sequential estimation, the methods of summation of random variables are used. To prove the asymptotic consistency of the confidence intervals of a fixed width, we used a method based on application of limit theorems for randomly stopped random processes. General conditions of the consistency and efficiency of sequential interval estimation of a wide class of functionals of an unknown distribution function are obtained and verified by sequential interval estimation of an unknown probability density of asymptotically uncorrelated and linear processes. Conditions of the regularity are specified that provide the property of being an estimate with an asymptotically minimum risk for a wide class of estimates and loss functions. Those conditions are verified by sequential point estimation of an unknown distribution function.

Robust Sequential Confidence Intervals for the Behrens–Fisher Problem*

1971 ◽  
Vol 20 (1-3) ◽  
pp. 77-82 ◽  
Author(s):  
Malay Ghosh
Keyword(s):  
Distribution Function ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Present Note ◽  
Rank Order ◽  
Sample Problem ◽  
Unknown Distribution ◽  
Two Sample Problem ◽  
Unknown Distribution Function ◽  
Rank Order Statistics

Summary The problem of providing a bounded length (sequential) confidence interval for the median of a symmetric (but otherwise unknown) distribution based on a general class of one-sample rank-order statistics was investigated in (Sen & Ghosh, 1971). The purpose of the present note is to indicate how the techniques developed there can be extended to the two-sample problem. It has been shown that in particular for the Behrens- Fisher situation (see e.g., Høyland, 1965 or Ramchandramurty, 1966), when the proposed procedure is based on the “normal-scores” statistic, under very general conditions on the unknown distribution function (d.f.), it is asymptotically at least as efficient as an analogous procedure suggested in (Robbins, Simons & Starr, 1967) and (Srivastava, 1970).

scholarly journals Distribution of Deoxynivalenol in Wheat, Wheat Flour, Bran, and Gluten, and Variability Associated with the Test Procedure

2003 ◽  
Vol 86 (3) ◽  
pp. 551-556 ◽  
Author(s):  
María M Samar ◽  
Constantino Ferro Fontán ◽  
Silvia L Resnik ◽  
Ana M Pacin ◽  
Marcelo D Castillo
Keyword(s):  
Distribution Function ◽  
Wheat Flour ◽  
Analytical Data ◽  
Test Procedure ◽  
Test Sample ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Normal Distribution Function ◽  
Type I ◽  
Distributional Information

Abstract Analytical data obtained on deoxynivalenol (DON) concentration in naturally contaminated wheat during processing in an industrial mill were statistically analyzed, and the distribution functions of DON concentration in lots of wheat, bran, wheat flour, and gluten were estimated. The analytical method had acceptable precision (HORRAT 0.25—0.32) for each test sample. The total variance combined sampling, sample preparation, and analytical variances were 0.188, 0.033, 0.42, and 0.0014 ppm2 for wheat, 1.93; flour, 0.99; bran, 4.68; and gluten, 0.29, respectively. The distribution function of DON contamination presented an asymmetric tail for high values of concentration in wheat grains and wheat flour; in bran it seemed to be bimodal with 2 separated peaks of different concentrations; in gluten the normal distribution function gave a reasonably good fit to empirical data. The function η(c) = –ln(–lnp), where p (c) is the cumulative distribution function was linear with c in the so-called extreme-value type I distribution and could be fitted by a cubic polynomial in c in the distributions determined for all the products. This variability and distributional information contributes to the design of better sampling plans in order to reduce the total variability and to estimate errors in the evaluation of DON concentration in lots of wheat and wheat products.

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