# lnreSich: generalized inverse Gauss-Poisson (GIGP, gamma = -0.5)

`lnreSich (-h -mW -kX -KY -EZ -H) text.spc`

The standard LNRE model based on the generalized inverse Gauss-Poisson distribution with gamma fixed at -0.5. Parameters are estimated using cost function C_1 as suggested in Sichel (1986).

input

`text.spc:` frequency spectrum

options

`-h:` display on-line help

`-mW:` number of ranks in fit is set to W (default: 15)

`-kX:` number of chunks for interpolation is set to X (default: 20)

`-KY:` number of chunks for extrapolation is set to Y (default: 20)

`-EZ:` extrapolation sample size is set to Z (default: 2N_0)

`-H:` input files do not have a header (default: with header)

output

`text_S.spc:` observed and expected frequency spectrum

`m:` m (frequency)

`Vm:` V(m,N) (frequency at sample size N)

`EVm:` E[V(m,N)] (expected frequency at sample size N)

`text_S.sp2:` expected frequency spectrum at 2N

`m:` m (frequency)

`EVm2N:` E[V(m,2N)] (expected frequency at sample size 2N)

`text_S.ev2:` vocabulary size statistics

`V:` V(N) (observed vocabulary size at N)

`EV:` E[V(N)] (expected vocabulary size at N)

`EV2N:` E[V(2N)] (expected vocabulary size at 2N)

`text_S.int, textS.ext:` interpolation and extrapolation statistics

`N:` N (number of tokens)

`E[V(N)]:` E[V(N)] (expected number of types)

`Alpha1:` E[alpha(1)] (E[V(1,N)]/E[V(N)])

`EV1-5:` E[V(1-5,N)] (expected spectrum elements)

`GV:` E[V(N+1)] - E[V(N)] (token-unit growth rate)

`text_S.sum:` summary statistics and estimated parameters

`N:` N (number of tokens)

`V(N):` V(N) (observed number of types)

`E[V(N)]:` E[V(N)] (expected number of types)

`V(1,N):` V(1,N) (observed number of hapax legomena)

`E[V(1,N)]:` E[V(1,N)] (expected number of hapax legomena)

`S:` S (population number of types)

`b:` b (parameter)

`c:` c (parameter)

`Z:` Z = 1/c (parameter)

`gamma:` gamma (parameter, fixed a-priori at -0.5)

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