== Truncating exponentials in MATLAB ==

Exponential distributions are useful because waiting times (for example between stimuli) follow an exponential distribution. 

Suppose we wish to produce 100 exponentially distributed random variables in the interval [Min, Max] with a given mean. (Min <= mean <= Max). Matlab code is given below to do this and illustrated with an example.

This is done in two stages. Firstly, compute m = (mean-min)/(max-min).

e.g. if min=100, max=200, mean=110 then m=0.1.

The below matlab code produces N=100 exponentially distributed random variables taking values between min=100 and max=200 with a mean of m.  Run the code by pasting this syntax, with required N, min, max and m, replaced by its numerical value, obtained as described above, at a command prompt in matlab. 
 

{{{
min=100;
max=200;
wout= inline('( (-exp(-x) ) / (1-exp(-x)) )*((x+1)/x) + 1/(x*(1-exp(-x)))- m',’x’);
N=100;
x = fzero(wout,1/m);
rand('state',sum(100*clock));
s=rand(1,N);
y = -log( 1- (1-exp(-x))*s )/x;
rv = min + y*(max-min);
hist(rv,(max-min)/10);
}}}

You can fit truncated regression models in R for example a truncated Normal distribution regression model can be fitted with the below code.

{{{
require(truncnorm)
require(truncreg)
 
x = (rtruncnorm(100, a = qnorm(.1, mean = 100, sd = 15), b=Inf, 
mean=100, sd=15))
sd(x)
tr.mod = truncreg(x ~ 1, direction = "left", point = min(x))
confint(tr.mod)
}}}

Output:

{{{
[1] 13.34503


               2.5 %    97.5 %
(Intercept) 97.65863 106.46516
sigma       12.31238  18.93937
}}}

A 95% confidence interval for mean from this truncated Normal distribution can also be computed as below.
{{{
t.test(x)$conf.int
}}}
Output:
{{{
[1] 102.3069 107.6028
attr(,"conf.level")
[1] 0.95
}}}