lossdw {DiscreteWeibull}

Loss function

Description

Loss function for the method of moments (type 1 discrete Weibull)

Usage

lossdw(par, x, zero = FALSE, eps = 1e-04, nmax=1000)

Arguments

par

vector of parameters q and \beta

x

the vector of sample values

zero

TRUE, if the support contains 0; FALSE otherwise

eps

error threshold for the numerical computation of the expected value

nmax

maximum value considered for the numerical computation of the expected value

Details

The loss function is given by L(x;q,\beta)=[m_1-\mathrm{E}(X;q,\beta)]^2+[m_2-\mathrm{E}(X^2;q,\beta)]^2, where \mathrm{E}(\cdot) denotes the expected value, m_1 and m_2 are the first and second order sample moments respectively.

Value

the value of the quadratic loss function

Author(s)

Alessandro Barbiero

See Also

Edweibull

Examples

x <- c(1,1,1,1,1,2,2,2,3,4)
lossdw(c(0.5, 1), x)
par <- estdweibull(x, "M") # parameter estimates derived by the method of moments
par
lossdw(par, x) # the loss is zero using these estimates