Question

please i want find that in R program very fast

find maxlike ,moment and probability weighed moment’s method for gumbel distrbution ( n=50,mu= 2,beta=4)

N= 1000

maxlikhood=mle

moment =mm

pwm=Probability weighed moment’s method

i want to use R studo program

find estimtate prarmeter to all method

also bias and MsE

Answer 1

To find the Exact Maximum Likelihood, the Inference for Margins, the Moment-base Estimation, and the Canonical Maximum Likelihood, we first require the package 'gumbel' in R/R-studio.

Then the following R code has to be run.

simu=rgumbel(50,params = list(location =2, scale =4))
simu
gumbel.MBE(simu[,1], simu[,2])
gumbel.IFM(simu[,1], simu[,2])
gumbel.EML(simu[,1], simu[,2])
gumbel.CML(simu[,1], simu[,2])

Explanation:

rgubmel generates 50 data with the location parameter value=2 and the scale parameter value=4.

So, putting n=50 and the location parameters values, we simulated our dataset.

It can be displayed by calling the assigned name simu.

gumbel.MBE gives the moment Based Estimation of the parameters.

gumbel.IFM gives the inference for the margins.

gumbel.EML gives the Exact Maximum Likelihood Estimations of the parameters.

gumbel.CML gives the Canonical Maximum Likelihood estimations of the parameters.

From the simulation alone, the Bias along with the MSE cannot be found.

Thank you.