A Saddlepoint Approximation of the Survival Functions of a Linear Combination of i.i.d. Chi-Square Random Variables = التقريب بطريقة نقطة السرج Saddlepoint لتركيبة خطية من متغيرات مربع توزيع كاي المستقلة

2020 ◽  
Vol 5 (1) ◽  
pp. 70-81
Author(s):  
Al Mutairi , Alya
Keyword(s):  
Linear Combination ◽  
Random Variables ◽  
Saddlepoint Approximation ◽  
Survival Functions ◽  
Chi Square

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

Continuity for multi-type branching processes with varying environments

1999 ◽  
Vol 36 (01) ◽  
pp. 139-145 ◽  
Author(s):  
Owen Dafydd Jones
Keyword(s):  
Linear Combination ◽  
Branching Process ◽  
Branching Processes ◽  
Random Variables ◽  
Main Tool ◽  
Concentration Function ◽  
Independent Random Variables ◽  
Varying Environments

Conditions are derived for the components of the normed limit of a multi-type branching process with varying environments, to be continuous on (0, ∞). The main tool is an inequality for the concentration function of sums of independent random variables, due originally to Petrov. Using this, we show that if there is a discontinuity present, then a particular linear combination of the population types must converge to a non-random constant (Equation (1)). Ensuring this can not happen provides the desired continuity conditions.

scholarly journals The Application of the BSSD Iono-Free Linear Combination Method in the Processing of Aircraft Positioning

2019 ◽  
Vol 26 (3) ◽  
pp. 15-21
Author(s):  
Janusz Ćwiklak ◽  
Marek Grzegorzewski ◽  
Kamil Krasuski
Keyword(s):  
Linear Combination ◽  
Experimental Test ◽  
Combination Method ◽  
Dual Frequency ◽  
Chi Square ◽  
Internal Reliability ◽  
Navigation Data ◽  
Positioning Method ◽  
Gps System ◽  
Positioning Algorithm

Abstract The article presents the results of research into the use of the differentiation technique of BSSD (Between Satellite Single Difference) observations for the Iono-Free LC combination (Linear Combination) in the GPS system for the needs of aircraft positioning. Within the conducted investigations, a positioning algorithm for the BSSD Iono-Free LC positioning method was presented. In addition, an experimental test was conducted, in which raw observational data and GPS navigation data were exploited in order to recover the aircraft position. The examination was conducted for the Cessna 172 and the on-board dual-frequency receiver Topcon HiperPro. The experimental test presents the results of average errors of determining the position of the Cessna 172 in the XYZ geocentric frame and in the ellipsoidal BLh frame. Furthermore, the article presents the results of DOP (Dilution of Precision) coefficients, the test of the Chi square internal reliability test and the HPL and VPL confidence levels in GNSS precision approach (PA) in air transport. The calculations were performed in the original APS software (APS Aircraft Positioning Software) developed in the Department of Air Navigation of the Faculty of Aeronautics at the Polish Air Force University.

An empirical saddlepoint approximation based method for smoothing survival functions under right censoring

2019 ◽  
Vol 47 (2) ◽  
pp. 238-261 ◽  
Author(s):  
Pratheepa Jeganathan ◽  
Noroharivelo V. Randrianampy ◽  
Robert L. Paige ◽  
A. Alexandre Trindade
Keyword(s):  
Saddlepoint Approximation ◽  
Right Censoring ◽  
Survival Functions

scholarly journals Saddlepoint Approximation for Data in Simplices: A Review with New Applications

Stats ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 121-147
Author(s):  
Riccardo Gatto
Keyword(s):  
Random Variables ◽  
Saddlepoint Approximation ◽  
Sample Space ◽  
Circular Data ◽  
Mathematical Framework ◽  
Urn Model ◽  
Dirichlet Distributions ◽  
The Common ◽  
Novel Applications ◽  
New Applications

This article provides a review of the saddlepoint approximation for a M-statistic of a sample of nonnegative random variables with fixed sum. The sample vector follows the multinomial, the multivariate hypergeometric, the multivariate Polya or the Dirichlet distributions. The main objective is to provide a complete presentation in terms of a single and unambiguous notation of the common mathematical framework of these four situations: the simplex sample space and the underlying general urn model. Some important applications are reviewed and special attention is given to recent applications to models of circular data. Some novel applications are developed and studied numerically.

Approximations to densities in geometric probability

1980 ◽  
Vol 17 (01) ◽  
pp. 145-153 ◽  
Author(s):  
H. Solomon ◽  
M. A. Stephens
Keyword(s):  
Monte Carlo ◽  
Random Variables ◽  
Monte Carlo Sampling ◽  
Geometric Probability ◽  
Simple Approximation ◽  
Chi Square ◽  
Percentage Points ◽  
Random Polygons

Many random variables arising in problems of geometric probability have intractable densities, and it is very difficult to find probabilities or percentage points based on these densities. A simple approximation, a generalization of the chi-square distribution, is suggested, to approximate such densities; the approximation uses the first three moments. These may be theoretically derived, or may be obtained from Monte Carlo sampling. The approximation is illustrated on random variables (the area, the perimeter, and the number of sides) associated with random polygons arising from two processes in the plane. Where it can be checked theoretically, the approximation gives good results. It is compared also with Pearson curve fits to the densities.

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