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The MittagLeffleR package allows

MittagLeffleR::rml(n = 5.5 , tail = 0.8 , scale = 1)

but not

MittagLeffleR::rml(n = 5L , tail = 0.8 , scale = 1)

because it wants an numeric argument for n. That leads to unnecessary errors. Please, might it possible to allow integers as well?

Why do restrict the optimization to the interval (0,1000)? Why do you not just use the max-likelihood estimator for the exponential distribution which is really easy?

'MittagLeffleR::qml(0.01, 0.1)' leads to an error because of the uniroot()-function in MittagleffleR:::qml1().

you can fix it with:

qml1 <- function(p,tail,scale=1) {
x <- numeric(length(p))
for (i in 1:length(p)) {
qml_p <- function(t) {pml(exp(t),tail,scale) - p[i]}
x[i] <- stats::uniroot(qml_p, interval = c(log(10^-14),log(100)),
extendInt="yes", tol = 1e-14)$root
}
return(exp(x))
}

Why is the parameter transform for the tail parameter

-log(1.1/theta_orig[1] - 1)

and not

• log(1/theta_orig[1] - 1) ?

Putting a tail >1 in dml, pml and qml should not be allowed and a warning should appear!!

Putting a tail=1 in rml leads to wrong random numbers!!

The asymptotic distribution of the teststatistic is not a chi-squared one distribution. Wilks Theorem is not working here, since our parameter of interest (tail) lies under H_0 on the boundary. You should remove the p_values!! They are wrong.