CODEWITHSUNDEEP
rstatistics
user3394267
user3394267

Reputation: 11

Fitting the t distribution with 'fitdistr' in R

I have a set of data which are the percentages of claimed compensation being awarded to claimants in an earthquake, i.e. awarded values/claimed values. I want to model the distribution of these percentage values and used the fitdistr function in R to fit a t distribution with 1 degree of freedom.

The fitdistr returned m and s values as: 

98.82907933(0.08574821)

and

2.87906212(0.10310584).

Now what is the formula for my distribution here? The function that allows me to calculate a percentage value when I input a value for claim compensation? Is it the pdf for the standard t distribution?

Upvotes: 1

Views: 3193

Answers (2)

Ben Bolker
Ben Bolker

Reputation: 226182

Since the t distribution with 1 df is also called the Cauchy distribution, you can model e.g. the probability of a claim being greater than 200,000 via:

params <- list(location=98.82907933,scale=2.87906212)
with(params,pcauchy(x=2e5,location,scale,lower.tail=FALSE)) ## 4.58e-6

Just to double-check, we can confirm that the location parameter is also the median:

with(params,pcauchy(x=location,location,scale,lower.tail=FALSE)) ## 0.5

You could also as suggested above transform your data and use pt:

with(params,pt((2e5-location)/scale,1,lower.tail=FALSE))  ## same as above

You can use dt/dcauchy for probability densities, qt/qcauchy for quantiles (the results of qt will have to be transformed as z*scale+location).

Upvotes: 1

Murray Jorgensen
Murray Jorgensen

Reputation: 81

Strictly speaking the t distribution with 1 degree of freedom (AKA the Cauchy distribution) has no parameters that need to be fit. What fitdistr would be doing here is estimating the parameters of a location/scale transformation t = (x - m)/s in order that t best fits the t_1 distribution. Here x is the data.

Upvotes: 1

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