# power.soft: Statistical power of soft-thresholding Fisher's p-value... In TFisher: Optimal Thresholding Fisher's P-Value Combination Method

## Description

Statistical power of soft-thresholding Fisher's p-value combination test under Gaussian mixture model.

## Usage

 `1` ```power.soft(alpha, n, tau1, eps = 0, mu = 0) ```

## Arguments

 `alpha` - type-I error rate. `n` - dimension parameter, i.e. the number of input p-values. `tau1` - truncation parameter=normalization parameter. tau1 > 0. `eps` - mixing parameter of the Gaussian mixture. `mu` - mean of non standard Gaussian model.

## Details

We consider the following hypothesis test,

H_0: X_i\sim F_0, H_a: X_i\sim (1-ε)F_0+ε F_1

, where ε is the mixing parameter, F_0 is the standard normal CDF and F = F_1 is the CDF of normal distribution with μ defined by mu and σ = 1.

## Value

Power of the soft-thresholding Fisher's p-value combination test.

## References

1. Hong Zhang and Zheyang Wu. "Optimal Thresholding of Fisher's P-value Combination Tests for Signal Detection", submitted.

`stat.soft` for the definition of the statistic.
 ```1 2 3``` ```alpha = 0.05 #If the alternative hypothesis Gaussian mixture with eps = 0.1 and mu = 1.2:# power.soft(alpha, 100, 0.05, eps = 0.1, mu = 1.2) ```