Rayleigh Channel Pearson Chi Square Test 1.0

CHI2RAYLTEST: Single sample Pearson Chi Square goodness-of-fit statistical test to examine a null hypothesis of Rayleigh Channel.H=CHI2RAYLTEST(X,ALPHA) performs the particular case of Pearson Chi Squaretest to determine whether the null hypothesis of a Rayleigh channel realization is a reasonable assumption regarding the population distribution of a complex random sample X with the desired significance level ALPHA.H indicates the result of the hypothesis test according to the MATLAB rules of conditional statements:H=1 => Do not reject the null hypothesis at significance level ALPHA.H=0 => Reject the null hypothesis at significance level ALPHA. The Chi Square hypotheses and test statistic in this particular case are: Null Hypothesis: X is a base-band Rayleigh channel realization with unknown mean and variance.Alternative Hypothesis: X is not a Rayleigh channel realization.The complex random sample X is shifted by its estimated mean and normalized by its estimated standard deviation giving Rayleigh parameter b=1/sqrt(2).The test drops K factor of Rician distribution for K > -inf[dB], so that the random sample from a Rician channel realization will pass the test as well. The tested bins XP are chosen to give 10 tested bins with equal expected probability. These binssupply a sufficient statistic forLENGTH(X)>=100.Let E(x) be the expected frequency X falls within XP according to the Rayleigh distribution and O(x) be the observed frequency. The Pearson statistic, X2=SUM((E(x)-O(x))^2/E(x)) distributes Chi Square withLENGTH(XP)-2 degrees of freedom.The decision to reject the null hypothesis is taken when the P value (probability that Chi2 random value with length(XP)-2 degrees of freedom is greater than X2) is less than significance level ALPHA.X must be a complex row vector representing a random sample corresponding to a base-band channel realization.ALPHA must be a scalar.The function doesn't check the formats of X and ALPHA, as well as a number of the input and output parameters.Author: G. Levin, June, 2003.References:W. T. Eadie, D. Drijard, F. E. James, M Roos and B. Sadoulet, "Statistical Methods in Experimental Physics", North-Holland, Sec. Reprint, 1982.

Requirements:	No special requirements
Platforms:	Matlab
Keyword:	Degrees,  Distributes,  Dsumexox,  Falls,  Lengthxp,  Observed
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