powersolve {OptHoldoutSize}

Fit power law curve

Description

Find least-squares solution: MLE of (a,b,c) under model ⁠y_i = a x_i^-b + c + e_i⁠; e_i~N(0,y_var_i)

Usage

powersolve(
  x,
  y,
  init = c(20000, 2, 0.1),
  y_var = rep(1, length(y)),
  estimate_s = FALSE,
  ...
)

Arguments

x

X values

y

Y values

init

Initial values of (a,b,c) to start. Default c(20000,2,0.1)

y_var

Optional parameter giving sampling variance of each y value. Defaults to 1.

estimate_s

Parameter specifying whether to also estimate s (as above). Defaults to FALSE (no).

...

further parameters passed to optim. We suggest specifying lower and upper bounds for (a,b,c); e.g. lower=c(1,0,0),upper=c(10000,3,1)

Value

List (output from optim) containing MLE values of (a,b,c)

Examples

# Retrieval of original values
A_true=2000; B_true=1.5; C_true=0.3; sigma=0.002

X=1000*abs(rnorm(10000,mean=4))
Y=A_true*(X^(-B_true)) + C_true + rnorm(length(X),sd=sigma)

c(A_true,B_true,C_true)
powersolve(X[1:10],Y[1:10])$par
powersolve(X[1:100],Y[1:100])$par
powersolve(X[1:1000],Y[1:1000])$par
powersolve(X[1:10000],Y[1:10000])$par