randomOrderUniform

Generates pseudorandom order statistics from a uniform (0, 1) distribution.

Synopsis

randomOrderUniform(ifirst, ilast, n)

Required Arguments

int ifirst (Input)

First order statistic to generate.

int ilast (Input)

Last order statistic to generate. ilast must be greater than or equal to ifirst. The full set of order statistics from ifirst to ilast is generated. If only one order statistic is desired, set ilast = ifirst.

int n (Input)

Size of the sample from which the order statistics arise.

Return Value

An array of length ilast + 1 - ifirst containing the random order statistics in ascending order. The first element is the ifirst order statistic in a random sample of size n from the uniform (0, 1) distribution.

Description

Function randomOrderUniform generates the ifirst through the ilast order statistics from a pseudorandom sample of size n from a uniform (0, 1) distribution. Depending on the values of ifirst and ilast, different methods of generation are used to achieve greater efficiency. If ifirst = 1 and ilast = n, that is, if the full set of order statistics are desired, the spacings between successive order statistics are generated as ratios of exponential variates. If the full set is not desired, a beta variate is generated for one of the order statistics, and the others are generated as extreme order statistics from conditional uniform distributions. Extreme order statistics from a uniform distribution can be obtained by raising a uniform deviate to an appropriate power.

Each call to randomOrderUniform yields an independent event. This means, for example, that if on one call the fourth order statistic is requested and on a second call the third order statistic is requested, the “fourth” may be smaller than the “third”. If both the third and fourth order statistics from a given sample are desired, they should be obtained from a single call to randomOrderUniform (by specifying ifirst less than or equal to 3 and ilast greater than or equal to 4).

Example

In this example, randomOrderUniform is used to generate the fifteenth through the nineteenth order statistics from a sample of size twenty.

from __future__ import print_function
from numpy import *
from pyimsl.stat.randomOrderUniform import randomOrderUniform
from pyimsl.stat.randomSeedSet import randomSeedSet
from pyimsl.stat.writeMatrix import writeMatrix

randomSeedSet(123457)
r = randomOrderUniform(15, 19, 20)
print("The 15th through the 19th order statistics from a \n",
      "random sample of size 20 from a normal distribution")
writeMatrix("", r, column=True)

Output

The 15th through the 19th order statistics from a 
 random sample of size 20 from a normal distribution
 
1       0.6575
2       0.6802
3       0.6807
4       0.8177
5       0.8254