Re: determine the underlying distribution

On Sep 20, 9:45 pm, sas...@xxxxxxxxx wrote:
On Sep 20, 12:18 am, randovaro <randov...@xxxxxxxxx> wrote:



On Sep 20, 12:00 pm, sas...@xxxxxxxxx wrote:

Dear all,

Can someone tell me what is the underlying distribution in this
experiment.

An experiment was designed to evaluate whether or not rainfall can be
increased by treating clouds with silver iodide. Rainfall was measured
from 70 clouds, of which 40 were chosen randomly to be seeded with
silver iodide. The objective is to describe the effect that seeding
has on rainfall. The measurements are the amounts of rainfall in acre-
feet from the 70 clouds.

Seeded: 1645.6, 1197.8, 1156.0, 978.0, 703.4, 489.1, 430.0, 334.1,
274.7, 274.7, 255.0, 242.5, 200.7, 198.6, 129.6,119.0, 92.4, 90.6,
91.4, 97.5, 150.7, 450.2, 123.8, 234.6, 357.0, 109.6, 302.1, 670.5,
118.3, 115.3

Unseeded: 425.6, 154.0, 352.4, 395.5, 441.2, 254.3, 263.0, 277.8,
281.2, 268.5, 257.3, 299.1, 336.6, 329.0, 318.6,
312.3, 327.3, 341.5, 350.9, 204.9, 151.0, 245.7, 267.4, 275.2, 347.9,
304.9, 310.1, 205.8, 278.9, 425.7

I took the natural log of your data. The distribution of your
unseeded log-transformed data looks normal. The distribution of the
seeded log-transformed data looks almost... uniform?- Hide quoted text -

- Show quoted text -

Thnaks for your time and effort. I want to produce plots of this data:
estimates of pdf, cdf and quantile function for seeded and unseeded
clouds. Can you tell me how can i do that? And also can you tell me
why did you took a log of the data inorder to determine the underlying
distribution and how did you take the log?

Regards,

A log transform will ameliorate the impact of outliers in data that
are inherently skewed toward larger values, like your rainfall
measurements. I used SPSS to look at your data but I note from your
profile that you use SAS so of course use whatever software you're
comfortable with.

You'll be able to define/plot the pdf & cdf of the log-normal
distribution using the mean & standard deviation from the data.
Similarly the pdf & cdf of the log-uniform can be defined using the
min and max values. I'm not familiar with quantile functions but I
understand they're just the inverse of the cdf.

The distribution of the log-transformed seeded data confused me a bit
though. On the one hand the histogram looks uniform. On the other hand
the Q-Q plot using a uniform distribution as the baseline failed what
a former contributor to this ng would call the "inter-ocular traumatic
test".

I'd be interested to hear what the sci.stat.* regulars (who know their
stats much better than me) think. But it looks like a homework
problem which may explain their reticence.

.

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