The exact distribution of indefinite quadratic forms in noncentral normal vectors

1996 ◽  
Vol 48 (2) ◽  
pp. 381-394 ◽  
Author(s):  
Serge B. Provost ◽  
Edmund M. Rudiuk
Keyword(s):  
Quadratic Forms ◽  
Exact Distribution ◽  
Normal Vectors ◽  
Indefinite Quadratic

scholarly journals On approximating the distribution of indefinite quadratic expressions in singular normal vectors

2020 ◽  
Vol 15 (1) ◽  
pp. 61-86
Author(s):  
Akbar Mohsenipour ◽  
Serge B. Provost
Keyword(s):  
Quadratic Forms ◽  
Positive Definite ◽  
Approximation Technique ◽  
Density Functions ◽  
Gamma Density ◽  
Special Cases ◽  
The Difference ◽  
Normal Vectors ◽  
Step Algorithm ◽  
Indefinite Quadratic

General representations of quadratic forms and quadratic expressions in singular normal vectors are given in terms of the difference of two positive definite quadratic forms and an independentlydistributed linear combination of normal random variables. Up to now, only special cases have been treated in the statistical literature. The densities of the quadratic forms are then approximated with gamma and generalized gamma density functions. A moment-based technique whereby the initial approximations are adjusted by means of polynomials is presented. Closed form and integral formulae are provided for the approximate density functions of the quadratic forms and quadratic expressions. A detailed step-by-step algorithm for implementing the proposed density approximation technique is also provided. Two numerical examples illustrate the methodology.

scholarly journals The Equivalence of Quadratic Forms

1957 ◽  
Vol 9 ◽  
pp. 526-548 ◽  
Author(s):  
G. L. Watson
Keyword(s):  
Quadratic Forms ◽  
Indefinite Quadratic ◽  
Number Of Classes

The main object of this paper is to find the number of classes in a genus of indefinite quadratic forms, with integral coefficients, in k ≥ 4 variables, distinguishing for even k two cases, according as improper equivalence is or is not admitted.

scholarly journals Least positive value of non-homogeneous indefinite quadratic forms of signature −3

1991 ◽  
Vol 37 (3) ◽  
pp. 260-278 ◽  
Author(s):  
Satish K. Aggarwal ◽  
D.P. Gupta
Keyword(s):  
Quadratic Forms ◽  
Indefinite Quadratic

The exact distribution function of the ratio of two dependent quadratic forms

2017 ◽  
Vol 47 (21) ◽  
pp. 5227-5240
Author(s):  
Edmund Rudiuk ◽  
Aleksander Kowalski
Keyword(s):  
Distribution Function ◽  
Quadratic Forms ◽  
Exact Distribution ◽  
Exact Distribution Function

scholarly journals Strongly indefinite quadratic forms and wild algebras

1990 ◽  
Vol 26 (1) ◽  
pp. 341-351
Author(s):  
Nikolaos Marmaridis
Keyword(s):  
Quadratic Forms ◽  
Indefinite Quadratic

Irrational indefinite quadratic forms

1935 ◽  
Vol 2 (2) ◽  
pp. 176-177 ◽  
Author(s):  
S. Chowla
Keyword(s):  
Quadratic Forms ◽  
Indefinite Quadratic

scholarly journals Quadratic ideals, indefinite quadratic forms and some specific diophantine equations

2018 ◽  
Vol 36 (3) ◽  
pp. 173-192
Author(s):  
Ahmet Tekcan ◽  
Seyma Kutlu
Keyword(s):  
Diophantine Equation ◽  
Quadratic Forms ◽  
Diophantine Equations ◽  
Algebraic Properties ◽  
Integer Solutions ◽  
Indefinite Quadratic

Let $k\geq 1$ be an integer and let $P=k+2,Q=k$ and $D=k^{2}+4$. In this paper, we derived some algebraic properties of quadratic ideals $I_{\gamma}$ and indefinite quadratic forms $F_{\gamma }$ for quadratic irrationals $\gamma$, and then we determine the set of all integer solutions of the Diophantine equation $F_{\gamma }^{\pm k}(x,y)=\pm Q$.

scholarly journals On indefinite quadratic forms

1977 ◽  
Vol 29 (2) ◽  
pp. 355-361 ◽  
Author(s):  
Tsuneo TAMAGAWA
Keyword(s):  
Quadratic Forms ◽  
Indefinite Quadratic
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