10.1 The Chi-square Goodness of Fit Test. The general area of nonparametric statistical inference deals with statistical procedures such as hypothesis testing, point estimation and confidence intervals in problems where the parent distribution has no known functional form. For one reason or another, the chi-square goodness of fit test is considered to be in this area, and so we present it here....

Square is a multivariate quadratic encryption scheme proposed in 2009. It is a specialization of Hidden Field Equations by using only odd characteristic elds and also X as its central map. In addition, it uses embedding to reduce the number of variables in the public key. However, the system was broken at Asiacrypt 2009 using a di erential attack. At PQCrypto 2010 Clough and Ding proposed two n...

The distribution of linear combinations of independent chi-square random variables is intimately related with the distribution of quadratic forms in normal random variables [1, 6, 7, 8, 9, 10, 11, 13, 14] and thus it also appears as the limit distribution of quadratic forms in non-normal random variables. As such, this distribution has been studied by many authors [2, 4, 5, 6, 7, 8, 9, 10, 11, ...

We consider products of independent large random rectangular matrices with independent entries. The limit distribution of the expected empirical distribution of singular values of such products is computed. The distribution function is described by its Stieltjes transform, which satisfies some algebraic equation. In the particular case of square matrices we get a well-known distribution which m...

Dans une permutation, un record est maximum ou minimum, en partant de la droite gauche. Les éléments d’une permutation peuvent être classés deux types : les records (dits points extérieurs) et autres intérieurs). permutations sans point intérieur ont été étudiées sous le nom carrées. Ici, nous explorons ayant nombre fini intérieurs, dites quasi-carrées. Contrairement aux carrées, l’énumération ...