dec.objf: Objective function for numerically finding MLEs under LR.dec,...
In mlespera/BenGood: Assessing Goodness-of-Fit of Data to Benford's Law

Description Usage Arguments Details References See Also

dec.objf contains the (negative) objective function of the nonlinear programming problem used to compute the MLEs in LR.dec.

1	dec.objf(zs, freq)

`zs`	Numeric vector, defined as the difference in probabilities: z_i = p_i - p_{i+1}
`freq`	Vector of multinomial frequencies.

LR.dec computes the MLEs of the first significant digit probabilities numerically under the alternative H_1: p_1 ≥ p_2 … ≥ p_9 by solving the nonlinear programming problem:

maximize ∑ f_i*log(∑ z_j)

subject to constraints, where f_i is the frequency of the ith significant digit, and z_i = p_i - p_{i+1}. dec.objf contains the negative of this expression in order to adhere to standard minimization optimization procedure. See Lesperance et. al for further details.

Lesperance M, Reed WJ, Stephens MA, Tsao C, Wilton B (2016) Assessing conformance with Benford's Law: goodness-of-fit tests and simultaneous confidence intervals. PLoS one; 11(3). Wong, S. (2010) Testing Benford's Law with the first two significant digits. University of Victoria, Master's thesis.

LR.dec

mlespera/BenGood documentation built on May 18, 2019, 3:43 p.m.