# Calculating log liklihood: Zero value of likelihood function

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1. Apr 6, 2015

### kirti1604

Hello,
I am analysing hydrology data and curve fitting to check the best probability distribution among 8 candidate distribution. (2 and 3 parameter distributions)
The selection is based on the lowest AIC value.
While doing my calculation in excel, how is it suggested to treat very low (approx 0) likelihood function values which result in a log likelihood of zero?
Should I just delete those value to get an AIC?
They generally are very low or very high values (possibly outliers ) which cause undefined values of log likelihood.
(I can delete those values because they are actual recorded data)

I would appreciate if someone can suggest the treatment of such data which result in zero likelihood and the log of which cant be determined.

2. Apr 8, 2015

### Orodruin

Staff Emeritus
Can you give some more information on what your data is and what kind of distributions you are assuming for it? Naturally, very low likelihood indicates bad models in general.

3. Apr 13, 2015

### kirti1604

My data is stream flow data.
I am testing for 8 distributions: normal, lognormal, 3parameter log normal, generalised extreme value, gamma, gamma 3/pearson type 3, log pearson type 3, gumbel.
these candidate distributions are selected based on literature review.
Now just to outline the steps for calculation of log likelihood in excel.( I got an addin for the software called easyfit which has the pdfs for all the distributions i need)
for every data point i calculate the value of the likelihood function, using the density function.
so for any particular distribution, if I have 20 data points, i have 20 values of the likelihood function. then i take the log of each value.
then I calculate the summation of the 20 values
calculate the AIC value. using the formula
AIC=2k-2(summation log likelihood)
k is the no of parameters of distribution.

do the same step for all distributions using 2 for normal lognormal gamma and gumbel and 3 for the others i calculate 8 AIC values and select my distribution using the lowest AIC.

now the values which dont give a value of the likelihood function are generally very low or very high values of the dataset . But I cant reject them as they are not outliers
station 1 was working fine and it outlines the steps i am following.
station 7 is causing trouble with the very high value(442) for the year 1950 as can be seen
the columns next to it are checking the high hand low ouliers using the grubs test after log transforming my data. (test chosen from literature for streamflow analysis)
The 3 tables are the main tables for doing my loglikelihood calculation which I am concerned with
the functions i used require an addin that comes after installing easyfit on 32bit office 2010

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• ###### station 7 AIC.xlsx
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Last edited: Apr 13, 2015