(BUG) L function and its Simulation Envelope under the null (CSR) not close to 0

[weikang9009]

This issue is raised by a user of pointpats - Wei Xie.

The Simulation Envelope under the null of CSR built for the L function is nowhere near 0 (see the following figure), which is not right based on its definition.

[ljwolf]

I think the equation is implemented incorrectly.. It should read:

    support, kestimate = _k(pp, intervals, dmin, dmax, d).T
    lestimate = np.sqrt(kestimate / np.pi)
    return np.column_stack((support, lestimate))

This is the form on wikipeda and in spatstats.

[jGaboardi]

FWIW, this is the formulation found in O’Sullivan and Unwin (2010). I was going to add it into spaghetti before realizing it is not well-suited for networks.

• D. O’Sullivan and D. J. Unwin. Point Pattern Analysis, chapter 5, pages 121–156. John Wiley & Sons, Ltd, 2010. doi:10.1002/9780470549094.ch5.

[weikang9009]

I think the equation is implemented incorrectly.. It should read:

    support, kestimate = _k(pp, intervals, dmin, dmax, d).T
    lestimate = np.sqrt(kestimate / np.pi)
    return np.column_stack((support, lestimate))

This is the form on wikipeda and in spatstats.

I do not see a major difference between these two implementations - the only difference is that your implementation does not deduct the distance from the "normalized" L function. The current implementation in pointpats follows another routine (as pointed out by @jGaboardi ) and is also shown in the Wikipedia:

I think the main purpose is to make the interpretation more intuitive: under the null, the L function follows a horizontal line at 0.

We have found the bug and Serge has fixed it in #45. Another bug is introduced with this PR and it is supposed to be fixed in #46. I should have closed this issue (have been waiting for the close of the #46) - sorry if this induces any confusion.

[ljwolf]

I see! Feel free to close this then!

the only difference...

Right. The plotting correction is not the L function itself.

I understand the L with this adjustment is interpreted like the J but centered on zero.

I think this needs to be documented + given an option.

[weikang9009]

The equation is given in the example notebook for distance statistics. I will add the missing equations for the distance functions to the inline docstrings. Thanks for the suggestion.