# weight_by_delta: Find sum of weights for the LaGrange multiplier In mshasan/OPWeight: Optimal p-value weighting with independent information

## Description

Compute sum of weights for a given value of the LaGrange multiplier

## Usage

 ```1 2``` ```weight_by_delta(delta, alpha = 0.05, et, m, m1, tail = 1L, ranksProb, effectType = c("continuous", "binary")) ```

## Arguments

 `delta` Numeric value of the LagRange multiplier `alpha` Numeric, significance level of the hypothesis test `et` Numeric, mean effect size of the test statistics `m` Integer, totoal number of hypothesis test `m1` Integer, number of true alternative tests `tail` Integer (1 or 2), right-tailed or two-tailed hypothesis test. default is right-tailed test. `ranksProb` Numeric vector of the ranks probability of the covariate statistics given the effect size `effectType` Character ("continuous" or "binary"), type of effect sizes

## Details

To obtain the normalized weight, and to make sure that the sum of the weights is equal to the number of tests and the weights are positive, an optimal value of the LaGrange multiplier `delta` needed. This function will compute the weights for a given value of the LaGrange multiplier and provide the sum of the weights in return.

## Value

`sumWeight_per_delta` sum of weights per delta value

## Author(s)

 ``` 1 2 3 4 5 6 7 8 9 10``` ```# generate a sequence of delta delta <- seq(0, 1, .0001) # compute probability fiven effect covariates = runif(100, min = 0, max = 2.5) probs <- dnorm(covariates, mean = 0, sd = 1) # compute the sum of weights for each delta weightSum_by_delta <- sapply(delta, weight_by_delta, m = 100, m1 = 50, et = 2, ranksProb = probs, effectType = "continuous") ```