Attributes of exponential distribution

Here’s the plot for means of 1000 samples each with 40 trials.

library("ggplot2");

run <- function(n_trials,n){
  data = NULL;
  for(i in 1:n_trials){
    new_data = rexp(n,0.2);
    std = sd(new_data);
    #print(std);
    mu = mean(new_data);
    data = c(data,mu);
    #print(i);
    
    
  }
  ans_std=sd(data);
  ans_mu=mean(data);
  print("ans_std:");
  print(ans_std);
  print("ans_mu:");
  print(ans_mu);
  data;
  
  
}
plot_data = run(1000,40);

## [1] "ans_std:"
## [1] 0.8103587
## [1] "ans_mu:"
## [1] 4.960514

qplot(plot_data,geom = c("histogram"),binwidth = 0.1);

RESULT:

This distribution is a normal distribution. The center(mean) is printed above. So does standard deviation. The theoretical value for both is 5. The real value of mean is very close to the real ones. However the real value of standard deviation is deviated heaily from the theoretical value.

Here’s the simualtion and plot for 1 sample each with 1000 trials.

qplot(rexp(1000,0.2));

## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.

As you see , it’s not a bell-shape plot.