# Rayleigh Channel Pearson Chi Square Test 1.0

OS : Windows / Linux / Mac OS / BSD / Solaris

Script Licensing : Freeware

Created : Sep 15, 2007

Downloads : 5

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## CHI2RAYLTEST: Single sample Pearson Chi Square ...

test: 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 Square

test 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=0 => Reject the null hypothesis at significance level ALPHA.

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 bins supply a sufficient statistic for LENGTH(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 with

LENGTH(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.

H=CHI2RAYLTEST(X, ALPHA) performs the particular case of pearson Chi Square

test 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 bins supply a sufficient statistic for LENGTH(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 with

LENGTH(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.

**• MATLAB Release: R12. 1**

**Demands:****Rayleigh Channel Pearson Chi Square Test 1.0 scripting tags:**statistics probability, null, rayleigh channel, hypothesis, pearson, test, pearson chi square test, sample.

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