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I have a data set with a dependent right-censored variable distributed over the Beta distribution. Please do not offer flexsurv package. It is necessary to describe the function of my Beta distribution for use in the AFT regression survival model survreg. An example from the book M. Zhu, I substituted the functions known to me, but I can not describe the ratio of the first and second derivatives of the density function of the Beta distribution :

# Beta Distribution - User-defined code for 'survreg'
a = 1.2; b = 0.2

myb <- list (name = "beta",

init = function (x, weights, ...)
{
mean <- sum (x * weights) / sum (weights)
var <- sum (weights * (x - mean) ^ 2) / sum (weights)
c (mean, var)
},

density = function (x, parms)
{
  cbind (
  pb (x, shape1 = a, shape2 = b, ncp = 0), # F - Cumulative Distribution Function
  1 - pb (x, shape1 = a, shape2 = b, ncp = 0), # S = 1 - F - Survival Function
  db (x, shape1 = a, shape2 = b, ncp = 0), # f - Density Function
  ?, # f'/ f - the first derivative of the Density function
  ? # f''/ f - the second derivative of the Density function
)
},

quantile = function (p, parms)
qb(x, shape1 = a, shape2 = b, ncp = 0),

deviance = function (...)
stop("deviance residuals not defined")
)

I believe that this is due to the derivatives of the beta function, the gamma function, digamma & trigamma function in the base package r, but my Math level does not allow them to be applied.

Александр Родионов
  • 11
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  • I believe that to obtain the [first derivative](http://www.wolframalpha.com/input/?i=derivative+of++x%5E(a-1)(1-x)%5E(b-1)%2Fbeta(a,b)) and the [second derivative](http://www.wolframalpha.com/input/?i=second+derivative+of+x%5E(a-1)(1-x)%5E(b-1)%2Fbeta(a,b)) of the probability density function Beta distributions that contain the glorious Euler *Beta* function, you should refer to the shareware website **WolframAlpha**. – Александр Родионов Jul 05 '18 at 09:42

0 Answers0