Reverse arrangement test PDF

Calculates the probability density function for the reverse arrangement test

Calculates the distribution of reverse arrangements for a sequence of
length N.

References:
(1) Bendat, J.S., Piersol, A.G., 2010. Random Data: Analysis and
Measurement Procedures, 4th ed. John Wiley & Sons, New York.

(2) Dr. Dave Trindade. The Reverse Arrangement Test: A Simple Procedure
for Detecting Trends in Equipment Reliability. Applied Reliability
Tools Workshop October 12-13, 1995 Boston, MA
http://www.trindade.com/Artwork%201995%20RAT%20Boston.pdf

Inputs:
N - length of sequence. N must be >= 2.

Outputs:
A - number of possible reverse arrangements (RA's). Ranges from 0 to
(N)*(N-1)/2.
p - probability of each number of reverse arrangements occurring.
Same dimensions as A
data - structure containing additional variables
data.z - expresses A as a zscore (normalizes to zero mean and
standard deviation of 1
data.mu - mean of A
data.sig - standard deviation of A
data.Ncomp - equal to the number of comparisons performed by
the RA test. Equal to (N)*(N-1)/2.

Examples:

Example 1: Calculate the probability distribution for a sequence of
length 4. Value p*factorial(4) tells the number of occurrences of each A
reverse arrangements.

[p A data] = RAdist(4);
p =
0.0417 0.1250 0.2083 0.2500 0.2083 0.1250 0.0417
A =
0 1 2 3 4 5 6
p*factorial(4) =
1 3 5 6 5 3 1

Example 2: Calculate the lowest zscore that exceeds the 95th percentile
of the PDF

N=50; [p A data] = RAdist(N); pc = cumsum(p);
ind = find(pc > 0.975,1,'first');
data.z(ind) =
1.9490