# Question:Fitting a distribution to censored categorical data

## Question:Fitting a distribution to censored categorical data

Maple
I have a rather complex statistical problem and was wondering if Maple would be able help. For my Oxford University thesis I have conducted a survey which seeks to estimate respondents' values for a certain preference parameter (relative risk aversion, RRA). This parameter is continous, but my data is categorical, i.e. the parameter value of each respondent is only estimated as a range. There are eight such categories. What makes it more complex still, is that the data is censored. The lowest category has no lower limit, and the highest category has no upper limit. The actual categories are as follows: less than 0.5, 0.5-1.0, 1.0-1.5, 1.5-2.0, 2.0-3.0, 3.0-5.0, 5.0-7.5, greater than 7.5 What I want to find is the overall mean value for the sample. The two extreme categories make this problematic. One solution would be to fit a distribution to the data, e.g. a lognormal distribution. Does anyone know if this can be done in Maple, when the data set is categorical and censored and we don't know the mean or standard deviation? Or is Matlab, SPSS or Stata better suited? Also, is there a function to find out which distribution gives the best fit to the data? Any help will be truly appreciated.
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