Q2. What is the common method of estimation of a moment?
Similar to the moment estimators, the L-moment estimators can also be obtained by equating the population L-moments with the corresponding sample L-moments.
Q3. What is the method used to compute the MLE of R?
One of the method which can be used to compute the MLE of R by plug-in estimates, i.e. replacing right hand side of (21) by the corresponding MLEs of the different unknown parameters and computing the integration numerically.
Q4. What is the asymptotic distribution of the moment estimators?
Ifα̂ME and λ̂ME are the moment estimators of α and λ respectively, then √ n ( α̂ME − α, λ̂ME − λ ) , is asymptotically bivariate normally distributed with the mean vector 0 and the exact expression of the asymptotic dispersion matrix as given in Gupta and Kundu [11].
Q5. What is the life length of the r-out-of-n system?
In the context of order statistics and reliability theory, the life length of the r-out-of-n system is the (n− r + 1)-th order statistics in a sample of size n.
Q6. What is the distribution of the sum of n i.i.d. random variables?
2.4 Distribution of the SumSince the moment generating function of the generalized exponential distribution is not in a very convenient form, the distribution of the sum of n i.i.d. generalized exponential random variables can not be obtained very easily.
Q7. Why did the authors perform extensive simulations to compare the performances of the different estimators for different?
Due to that the authors performed [11] extensive simulations to compare the performances of the different estimators for different sample sizes and for different parameter values in terms of biases and mean squared errors.
Q8. What is the probability of a random variable being exponentiated?
The result can be stated as follows: If X1, . . . , Xn are i.i.d. random variables then Xi’s are exponentiated random variables if and only if the maximum of {X1, . . . , Xn} is an exponentiated random variable.