# Goodness of fit test for exponential distribution

#### Clarkson

##### New Member
The given data below shows the time in intervals in seconds between successive white cars in flowing traffic in an open road.Can these be modeled by an exponential distribution.

I am computing the expected frequencies by calculating the probability at each interval.Under null hypothesis as this follows an exponential distribution for the first category I integrated from 0-20.
Then Expected frequency for that category is Probability total frequency=0.3935*100.
The lamda value for the exponential distribution is found by supposing this equals sample mean.
Sample mean=Sigma f*x/Sigma f.
If this data follows an exponential distribution with parameter lamda as expected value=1/lamda,
1/lamda=(Sigma f*x)/(Sigma f) .
My H0 is Data follows an exponential distribution
My question is when I calculate Expected frequencies though the total should add up to 100 it does not do so because of rounding off errors right?I get a value of 98.89.
Here should I need to add another category myself as the interval being 180-infinity and get its expected value as 100-98.89=1.11.
Is it necessary to add this category as this is an exponential distribution which goes for infinity?Of course as the Expected value of the created category is less than 5, in this case I have to add this up with the upper category.But if I do not consider this new category then the degrees of freedom changes.Is it necessary to add this new category as 180-infinity

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