# spectfit: Naranan-Balasubrahmanyan smoother, Good-Turing estimation

`spectfit (-h -mW -H -eR -n -v) text.spc`

This program fits the Naranan-Balasubrahmanyan model and computes Good-Turing estimates.

input

`text.spc:` frequency spectrum

options

`-h:` display on-line help

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

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

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

`-v:` include |V(N)-E[V(N)]| in cost function

`-n:` include |N-Nfit| in cost function

output

`text_N.spc:` observed and expected frequency spectrum

`m:` m (frequency)

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

`SVm:` V_{r}(m,N) (real-valued spectrum)

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

`mStar:` m* (Good-Turing estimate using E[V(m,N)])

`mStarRaw:` m* (Good-Turing estimate using V_{r}(m,N)))

`StdevMstar:` standard deviation of m*

`text_N.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(m,N):` V(m,N)

`E[V(m,N)]:` E[V(m,N)]

`C:` C (first parameter)

`mu:` mu (second parameter)

`gamma:` gamma (third parameter)

`MSE:` mean squared error

`Nfit:` sum_m mE[V(m,N)]

`Nproxy:` sum_{m=1}^{mmax} mV_{r}(m,N)

`Vproxy:` sum_{m=1}^{mmax} V_{r}(m,N)

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