README.Rmd

---
output: github_document
---

<!-- README.md is generated from README.Rmd. Please edit that file -->

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "man/figures/README-",
  out.width = "100%"
)
```

# solvetruncated

<!-- badges: start -->
[![R-CMD-check](https://github.com/BjarkeHautop/solvetruncated/actions/workflows/R-CMD-check.yaml/badge.svg)](https://github.com/BjarkeHautop/solvetruncated/actions/workflows/R-CMD-check.yaml)
<!-- badges: end -->

# Overview 

The goal of solvetruncated is to solve for parameters of truncated distributions
given desired mean and value of CDF at a point. It does this by numerical optimization.

This is for example useful for when 
specifying a prior in Bayesian, where your belief is often with respect to a mean and 
value of CDF at a point. 

## Installation

You can install the development version of solvetruncated from [GitHub](https://github.com/) with:

``` r
# install.packages("devtools")
devtools::install_github("BjarkeHautop/solvetruncated")
```

## Example

Here is an example where we wish to solve for the parameters
$(\mu, \sigma)$ of
$$X \sim \text{TruncNormal}(\mu, \sigma, a=0, b=\infty),$$ where we wish to have
$E[X]=0.5$ and $P(X\leq 0.75)=0.8$.

```{r example}
library(solvetruncated)
solve_truncated_normal(desired_mean = 0.5, x_value = 0.75, desired_prob = 0.8, a = 0, b = Inf)
```

which gives that the parameters should be $(\mu=0.42, \sigma=0.35)$.