# lnreYuSi: Yule-Simon

`lnreYuSi (-h -mW -kX -KY -EZ -H -eR -sS -Nn -Vn -P) text.spc`

The standard Yule-Simon LNRE model. Since there are no closed-form expressions for estimating the parameters of theYule-Simon model, the program asks the user whether to use downhill simplex minimization or to provide interactive user-guided minimization. In the case downhill simplex minimization is selected, the program asks for initial values for Z, beta, and V(Z). A reasonable starting point is (200,0.5,150). By default, cost function C_1 is used, but cost function C_{2}(r) can be selected as well using the -e option.

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)

`-eR:` use cost function C_{2}(r) with r=R

`-sS:` calculate only the expected spectrum for S ranks, output on textY.fsp

`-Nn:` force N to equal n (in case of a partial spectrum)

`-Vv:` force V(N) to equal v (in case of a partial spectrum)

`-P:` estimate V(Z) from m* instead of including V(Z) as third parameter

output

`text_Y.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_Y.fsp:` expected frequency spectrum

`m:` m (frequency)

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

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

`m:` m (frequency)

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

`text_Y.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_Y.int, text_Y.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_Y.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)

`Z:` Z (parameter)

`beta:` beta (parameter)

`VZ:` V(Z) (parameter)

`S:` S (population number of types)

technical details

The integrals of the Yule-Simon model are evaluated by means of Rombergintegration for the interval [0.000001, 10000.0], using the subroutine qromb of Press et al. (1988). The downhill simplex minimization method is used for parameter estimation, using the subroutine amoeba of Press et al. (1988).

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