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Double-normal selectivity as a function of length (SS3 pattern 24, full form)

sel_double_normal.Rd

All parameters are on the real line, making this parameterization suitable for unconstrained optimization and AD. The length-bin vector x is used to define natural scales for position and width parameters.

Usage

sel_double_normal(x, par)

Arguments

x

Numeric vector of length-bin midpoints.

par

Numeric vector of length 6 containing selectivity parameters.

par[1] (a)

Peak location (real line). Transformed via mean(x) + a * sd(x), so a = 0 places the peak at mean(x).

par[2] (b)

Plateau width (real line). Controls the distance from peak to the start of the descending limb via logistic transform of the available range: peak + bin_width + (0.99 * max(x) - peak - bin_width) / (1 + exp(-b)).

par[3] (c)

Ascending width (real line, log-space). Actual width = exp(c) * sd(x). c = 0 gives an ascending width equal to sd(x).

par[4] (d)

Descending width (real line, log-space). Actual width = exp(d) * sd(x). d = 0 gives a descending width equal to sd(x).

par[5] (e)

Initial selectivity (real line, logit-space). Transformed via 1 / (1 + exp(-e)), so e = 0 gives initial selectivity of 0.5, large negative values give ~0, large positive values give ~1.

par[6] (f)

Final selectivity (real line, logit-space). Same transform as e.

Value

Numeric vector of selectivity values in [0, 1].

Details

Only the full form is implemented (e and f both active). The simplified forms where e <= -999 or f <= -999 are not supported.