We introduce two methods for approximation to distribution of weighted sum of chi-square random variables. These methods can be more useful than the known methods in literature to transform chi-square type chance constrained programming (CCP) problem into deterministic problem. Therefore, these are compared with Sengupta (1970)’s method. Some examples are illustrated for the purpose of comparin...

One of the many techniques which has recently been employed for filtering spam is one described in the Linux Journal article A Statistical Approach to the Spam Problem [Robinson]. This technique incorporates ideas from the seminal article A Plan For Spam [Graham] as well as R.A. Fisher's technique for combining p-values by means of the chi-square distribution [Hedges & Olkin]. The technique pre...

A new probabilistic shaping distribution that outperforms Maxwell-Boltzmann is studied for the nonlinear fiber channel. Additional gains of 0.1 bit/symbol MI or 0.2 dB SNR for both DP-256QAM and DP-1024QAM are reported after 200 km nonlinear fiber transmission. OCIS codes: (060.0060) Fiber optics and optical communications; (060.1660) Coherent communications.

The properties of the ground state of liquid He are studied using a correlated basis function of the form ∏ i<j ψ(rij). Here, ψ(r) is chosen as the exact solution of the Schrödinger equation for two He atoms. A hard-sphere plus an attractive square well is used as the interaction potential between He atoms. The pair distribution function is calculated using approximate integral methods, namely ...

In cognitive radio, spectrum sensing is a challenging task. In this letter, a new spectrum sensing method is proposed based on Goodness of Fit test (GoF) of the energy of the received samples with a chi-square distribution. We derive the test statistic and evaluate the performance of the proposed method by Monte Carlo simulations. It is shown that our proposed spectrum sensing method outperform...

Since density is considered as one of the most important numerical indices to explain quantitative values of a plant community by affecting on many aspects and activity of ecosystem, on the other hand, awareness about plants distribution pattern in environment is an essential preparation for measurement and study of vegetative cover, therefore, in this research determination of density and dist...

A test for goodness of fit usually involves examining a random sample from some unknown distribution in order to test the null hypothesis that the unknown distribution function is in fact a known, specified function. The Chi-square test can be applied to any univariate distribution for which you can calculate the cumulative distribution function. The Chi-square test does not have good propertie...

The multivariate asymptotic distribution of sequential Chi-square test statistics is investigated. It is shown that: (a) when sequential Chi-square statistics are calculated for nested models on the same data, the statistics have an asymptotic intercorrelation which may be expressed in closed form, and which is, in many cases, quite high; and (b) sequential Chi-square difference tests are asymp...

Standardizing the empirical distribution function yields a statistic with norm square that matches the chi-square test statistic. To show this one may use the covariance matrix of the empirical distribution which, at any finite set of points, is shown to have an inverse which is tridiagonal. Moreover, a representation of the inverse is given which is a product of bidiagonal matrices correspondi...

Since density is considered as one of the most important numerical indices to explain quantitative values of a plant community by affecting on many aspects and activity of ecosystem, on the other hand, awareness about plants distribution pattern in environment is an essential preparation for measurement and study of vegetative cover, therefore, in this research determination of density and dist...