fritools (version 4.6.0)

sloboda: Sloboda's Growth Function

Description

Implement the growth function $$ y_t = k^{\beta_{1}} \times \left(\frac{y_0}{k^{\beta_{1}}}\right)^{\exp \left[ \frac{\beta_{2}}{(\beta_{3}-1) \times t ^{(\beta_{3}-1)}} - \frac{\beta_{2}}{(\beta_{3}-1) \times t_0 ^{(\beta_{3}-1)}} \right] } $$ published in Sloboda, B., 1971: Zur Darstellung von Wachstumsprozessen mit Hilfe von Differentialgleichungen erster Ordnung. Mitt. d. Baden-Württembergischen Forstlichen Versuchs- und Forschungsanstalt.

Usage

sloboda(a, b, c, y0, t0, t, type = c("classic", "kaendler"), k = 65)

Value

The value \(y_t\) of Sloboda's growth function.

Arguments

a

Sloboda's \(\beta_{3}\).

b

Sloboda's \(\beta_{2}\).

c

Sloboda's \(\beta_{1}\).

y0

Sloboda's \(y_{0}\).

t0

Sloboda's \(t_{0}\).

t

Sloboda's \(t\).

type

Gerald Kaendler reformulated the algorithm, but it doesn't get faster, see the examples.

k

Sloboda's \(k\).

See Also

Other statistics: column_sums(), count_groups(), powers_of_ten, relative_difference(), round_half_away_from_zero(), weighted_variance()

Examples

microbenchmark::microbenchmark(cl = sloboda(0.2, 0.7, 3, 30, 30, 35),
                               g =  sloboda(0.2, 0.7, 3, 30, 30, 35,
                                            "kaendler"),
                               check = "equivalent")