Question

In: Statistics and Probability

Use R and perform following: Generate 1000 observations from an exponential distribution with mean 10. Generate...

Use R and perform following:

Generate 1000 observations from an exponential distribution with mean 10.
Generate 1000 observations from a central t-distribution with 8 degree of freedom.
Make a qqplot of observations in problem 1 versus quantiles generated from a t-distribution
with 8 degree of freedom. Can the t distribution be used to approximate data in part 1?Submit
the plot.
Repeat above part but submit a qqplot of the observations in 1 versus quantiles from an exponential
with mean 1. What is your conclusion?

Expert Solution

Random exponential distribution in R:-

For generating random exponential distribution in R is rexp(n,lamda) where n refers to the sample size and lambda is the rate parameter. The mean of exponential distribution is 1/lambda and the standard deviation is also 1/lambda

rexp(n,lamda)

>x<- rexp(1000, 0.1)

>x[0:20]

[1] 11.8374577  0.6041982  2.6490437  4.5841595 33.2941223 11.1561669
 [7] 12.0257420  2.4585212  0.5783512 22.8702997  2.6110438  8.5349925
[13] 23.9149159  3.8423621  8.8366142 11.0909087  5.4228406  5.6150966
[19]  7.9317064 16.0707504

Random t distribution in R:-

rt(a,b) returns a random draws from a t distribution centered at 0 with b degrees of freedom.

rt(a,b)

>y <- rt(1000,8)

>y[0:20]

[1] -1.855119123  0.802409732 -0.366512326  0.348991110 -0.889810771
 [6]  1.316007092  1.243631552 -3.505593271 -0.181419213  0.654032170
[11]  1.156344566 -0.556387657 -0.669780166  0.236448825  1.071076264
[16]  0.472816531  0.004414854 -0.471919606 -1.579729421  0.529356835

qqplot-

>qqplot(x,y)

qqplot of observations in problem 1 versus quantiles generated from a t-distribution
with 8 degree of freedom

>qqplot(y,x)

qqplot of the observations in 1 versus quantiles from an exponential

It data follows straight line means >> normally distributed

orchestra answered 1 year ago

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