lnreCarr: lognormal


lnreCarr (-h -mW -kX -KY -EZ -H -eR -sS -Nn -Vv) text.spc

The standard LNRE model based on the lognormal distribution. Since there are no closed-form expressions for estimating the parameters of the lognormal 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 calculates E[V(N)] and for Z=200 and sigma = 1.5. The user is offered the choice between using these parameters as starting point for minimization, or to specify another starting point. By default, cost function C_1 is used. In order to use cost function C_{2}(r), use 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: header is presupposed)

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

    -sS: calculate only the expected spectrum for S ranks, output on textC.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)

output

    text_C.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_C.fsp: expected frequency spectrum

          m: m (frequency)

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

    text_C.sp2: expected frequency spectrum at 2N

          m: m (frequency)

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

    text_C.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_C.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 = e^{-mu} (parameter)

          mean: mu (mean)

          stdev: sigma (standard deviation)

          S: S (population number of types)

    text_C.int, text_C.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)

technical details

The integrals of the lognormal model are evaluated by means of Rombergintegration for the interval [0.000001, 1000.0], 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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