Description Usage Arguments Details Value Author(s) References Examples
First and second order moments, variance and expected value of the reciprocal for the type 1 discrete Weibull distribution
1 2 3 4 |
q |
first parameter |
beta |
second parameter |
eps |
error threshold for the numerical computation of the expected value |
nmax |
maximum value considered for the numerical approximate computation of the expected value; |
zero |
|
The expected value is numerically computed considering a truncated support: integer values smaller than or equal to 2F^{-1}(1-eps;q,β) are considered, where F^{-1} is the inverse of the cumulative distribution function (implemented by the function qdweibull
). However, if such value is greater than nmax
, the expected value is computed recalling the formula of the expected value of the corresponding continuous Weibull distribution (see the reference), adding 0.5. Similar arguments apply to the other moments.
the (approximate) expected values of the discrete Weibull distribution:
Edweibull
gives the first order moment, E2dweibull
the second order moment, Vdweibull
the variance, ERdweibull
the expected value of the reciprocal (only if zero
is FALSE
)
Alessandro Barbiero
M. S. A. Khan, A. Khalique, and A. M. Abouammoh (1989) On estimating parameters in a discrete Weibull distribution, IEEE Transactions on Reliability, 38(3), pp. 348-350
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | q <- 0.75
beta <- 1.25
Edweibull(q, beta)
E2dweibull(q, beta)
Vdweibull(q, beta)
ERdweibull(q, beta)
# if beta=0.75...
beta <- 0.75
Edweibull(q, beta)
Edweibull(q, beta, nmax=100)
# here above, the approximation through the continuous model intervenes
# if beta=1...
beta <- 1
Edweibull(q, beta)
# which equals...
1/(1-q)
|
Loading required package: Rsolnp
[1] 3.037885
[1] 13.3628
[1] 4.134054
[1] 0.4976714
[1] 6.806787
[1] 6.769456
[1] 4
[1] 4
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