nav[aria-label="Primary Navigation"] { padding: 0; & ul { list-style: none; width: 100%; display: flex; flex-direction: row; justify-content: start; align-items: start; gap: 30px; padding: 0; & li { margin: 0; } & ul li { list-style: none; } } }

Does anyone know about Ripley's K-Function and how to use it in JMP?

martindemel

A customer of mine (Qiagen) asked for this special analysis (Ripley's K-Function): http://resources.esri.com/help/9.3/arcgisdesktop/com/gp_toolref/spatial_statistics_tools/how_multi_distance_spatial_cluster_analysis_colon_ripley_s_k_function_spatial_statistics_works.htm

He wants to use it to verify that the distribution on a wafer/chip is random, the base for be able to use Poisson distribution to back-calculate.

thanks for any input,

Martin

Accepted answers

Daniel_Valente

The R package Spatstat also performs this: https://cran.r-project.org/web/packages/spatstat/vignettes/getstart.pdf. Could use the JMP interface to R to perform this analysis should the user not have access to MATLAB or SAS.

All comments

Chris_Kirchberg

Hi Martin,

I cannot find anything on the internet that would help as far as anyone implementing within JMP. I have see references to ESRI and other software used by GIS people, but nothing within JMP itself.

ian_jmp

You could use the MATLAB integration, else translate the code below to JSL.

function K = RipleysK(locs,dist,box,method);
% RipleysK: Calculate K statistic
% 
% K = RipleysK(locs,dist, box,method) calculates G, the K statistic at each 
% distance for the data with x-y coordinates given by locs, and the
% bounding rectangle given by box=[minX maxX minY maxY].
% If method=0, no edge correction is applied.
% If method=1, points are only used if they are at least h units away from
% the edge.
%
% Note: The L statistic may be calculated from the K statistic as follows: 
%   L = sqrt(K/pi)-h;
%   

if nargin<4, method=1; end
[N,k] = size(locs);
if k~=2, error('locs must have two columns'); end
rbox = min([locs(:,1)'-box(1);box(2)-locs(:,1)';locs(:,2)'-box(3); box(4)-locs(:,2)'] );
% rbox is distance to box

DX = repmat(locs(:,1),1,N)-repmat(locs(:,1)',N,1);
DY = repmat(locs(:,2),1,N)-repmat(locs(:,2)',N,1);
DIST = sqrt(DX.^2+DY.^2);
DIST = sort(DIST);

if method==1
K = zeros(length(dist),1);
for k=1:length(K)
    I = find(rbox>dist(k));
    if length(I)>0
        K(k) = sum(sum(DIST(2:end,I)<dist(k)))/length(I);
    end
end
elseif method==0
    K = zeros(length(dist),1);
    for k=1:length(K)
        K(k) = sum(sum(DIST(2:end,:)<dist(k)))/N;
    end
end

lambda = N/((box(2)-box(1))*(box(4)-box(3)));
K = K/lambda;

stan_koprowski

You can also do this in SAS using Proc SPP

This procedure has the edge corrections, Ripley's k function and more.

K <(UNPACK)>
produces a panel of Ripley’s K function. The K function is the ratio of the expected number of point pattern observations within distance r of any other observation divided by the average intensity value of the point pattern. The panel contains four plots: an EDF plot that shows simulation envelopes for CSR, an EDF-CSR difference plot, a PP plot that compares the EDF of the summary statistic, and a confidence interval plot that shows envelopes for the confidence intervals of the summary statistic.
The K plot is produced when you specify the K option in the PROCESS statement. If you specify PLOTS=K without specifying the K option in the PROCESS statement, then PLOTS=K is ignored. You can specify the following option:
UNPACK
suppresses paneling of the K function plots and produces each constituent plot separately.

Daniel_Valente

martindemel

Thanks to all replies, very helpful!!!

The R package might be the best approach as it is open source.

Thanks,

Maritn