
ORDER STATISTICS MEDIANSName:
UNIFORM HALF NORMAL EV1 (or GUMBEL) EV2 (or FRECHET) WEIBULL EXPONENTIAL
Order statistics are commonly used in extreme value analysis. In particular, the first (i.e., minimum) and nth (i.e., maximum) order statistics are of interest. The order statistic medians (Filliben 1975) can be approximated by:
where U_{i} are the uniform order statistic medians (defined below) and G is the percent point function for the desired distribution. The uniform order statistic medians are defined as:
m_{i} = (i  0.3175)/(n + 0.365) for i = 2, 3, ..., n1 m_{i} = 0.5^{(1/n)} for i = n Dataplot uses order statistic medians in the generation of probability plots. Specifically, the probability plot is formed by:
FOR I = <start> <inc> <stop> where <dist> identifies the distribution from which the order statistics are derived (NORMAL, HALF NORMAL, UNIFORM, EV1, EV2, WEIBULL, EXPONENTIAL); <start> is a number or parameter that identifies the first row of <resp> in which the order statistics medians are saved (typically it has a value of 1); <inc> is a number or parameter that identifies the row increment of <resp> in which the order statistics medians are saved (typically it has a value of 1); <stop> is a number or parameter that identifies the last row of <resp> in which the order statistics medians are saved; and where <resp> is a variable where the order statistics medians are saved.
LET Y2 = NORMAL ORDER STATISTICS MEDIANS FOR I = 1 1 1000 LET Y1 = HALF NORMAL ORDER STATISTICS MEDIANS FOR I = 1 1 100 LET Y1 = UNIFORM ORDER STATISTICS MEDIANS FOR I = 1 1 100 LET Y1 = EV1 ORDER STATISTICS MEDIANS FOR I = 1 1 100
LET GAMMA = 3.2
LET GAMMA = 2
LET YTEMP = UNIFORM ORDER STATISTIC MEDIANS FOR I = 1 1 100 LET YOSMED = GAMMPPF(YTEMP,GAMMA)
GUMBEL for EV2
1993/05: Added EV1 (Gumbel), EV2 (Frechet) and Weibull distributions 2022/04: Added exponential distribution SKIP 25 READ ZARR13.DAT Y LET N = SIZE Y LET Y = SORT Y LET X = ORDER STATISTIC MEDIANS FOR I = 1 1 N . TITLE CASE ASIS LABEL CASE ASIS TITLE Normal Probability Plot for ZARR13.DAT Y1LABEL Sorted Data X1LABEL Normal Order Statistic Medians . PLOT Y X  
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Date created: 04/08/2022 