estimationFunction: Estimation of p and q for [p,p,p,q]-model

In FractalParameterEstimation: Simulation and Parameter Estimation of Randomized Sierpinski Carpets using the p-p-p-q-Model

Description

This function combines all used functions (potence, increment, fillMatrix, calcRamification, createSmallerMatrix) of R-Package and estimates the parameters p and q on the basis of a [p,p,p,q]-model. This model is based on randomized Sierpinski-Carpet, where the two parameters can be chosen independently. It returns value for p and q in a list. The estimation procedure only works for data consisting of zeros and ones, which are representing values for white and areas of for instance mammographic screening of breast tissue. Parameters p and q are estimated independently, both on basis of the impact of one ramification step.

Usage

estimationFunction(daten, decs)

Arguments

daten	Data consisting of either 0 or 1 for every cell, where number of rows must equal to number of columns
decs	Number of decimal places to be rounded. Default value is 4.

Value

p-Estimator	Estimator of p for first three iterations of [p,p,p,q]-model on basis of the third step
q-Estimator	Estimator of q for last step in procedure of [p,p,p,q]-model

Author(s)

Philipp Hermann; Jozef Kiselak; Milan Stehlik\ [e-mail]; [e-mail]; [e-mail]

References

Hermann, P., Mrkvicka, T., Mattfeldt, T., Minarova, M., Helisova, K., Nicolis, O., Wartner, F., and Stehlik, M. (2015). Fractal and stochastic Geometry Inference for Breast Cancer: a Case Study with Random Fractal Models and Quermass-Interaction Process. Statistics in Medicine, 34(18), 2636-2661. doi: 10.1002/sim.6497.

Examples

## Example 1: Original p-Value: 0.2; Original q-value: 0.1
estimationFunction(Data0201, decs = 2)

## Example 2: Original p-value: 0.3; Original q-value: 0.25
estimationFunction(Data03025) # testData2

## Example 3: Original p-value: 0.5; Original q-value: 0.1
estimationFunction(Data0501)

## Example 4: Original p-value: 0.6; Original q-value: 0.3
estimationFunction(Data0603)

FractalParameterEstimation documentation built on July 10, 2019, 5:05 p.m.