# ciLRx: Likelihood Ratio method of CI estimation In proportion: Inference on Single Binomial Proportion and Bayesian Computations

## Description

Likelihood Ratio method of CI estimation

## Usage

 `1` ```ciLRx(x, n, alp) ```

## Arguments

 `x` - Number of successes `n` - Number of trials `alp` - Alpha value (significance level required)

## Details

Likelihood ratio limits for the given `x` and `n` obtained as the solution to the equation in `p` formed as logarithm of ratio between binomial likelihood at sample proportion and that of over all possible parameters

## Value

A dataframe with

 `x ` - Number of successes (positive samples) `LLRx ` - Likelihood Ratio Lower limit `ULRx ` - Likelihood Ratio Upper Limit `LABB ` - Likelihood Ratio Lower Abberation `UABB ` - Likelihood Ratio Upper Abberation `ZWI ` - Zero Width Interval

## References

[1] 1993 Vollset SE. Confidence intervals for a binomial proportion. Statistics in Medicine: 12; 809 - 824.

[2] 1998 Agresti A and Coull BA. Approximate is better than "Exact" for interval estimation of binomial proportions. The American Statistician: 52; 119 - 126.

[3] 1998 Newcombe RG. Two-sided confidence intervals for the single proportion: Comparison of seven methods. Statistics in Medicine: 17; 857 - 872.

[4] 2001 Brown LD, Cai TT and DasGupta A. Interval estimation for a binomial proportion. Statistical Science: 16; 101 - 133.

[5] 2002 Pan W. Approximate confidence intervals for one proportion and difference of two proportions Computational Statistics and Data Analysis 40, 128, 143-157.

[6] 2008 Pires, A.M., Amado, C. Interval Estimators for a Binomial Proportion: Comparison of Twenty Methods. REVSTAT - Statistical Journal, 6, 165-197.

[7] 2014 Martin Andres, A. and Alvarez Hernandez, M. Two-tailed asymptotic inferences for a proportion. Journal of Applied Statistics, 41, 7, 1516-1529

`prop.test and binom.test` for equivalent base Stats R functionality, `binom.confint` provides similar functionality for 11 methods, `wald2ci` which provides multiple functions for CI calculation , `binom.blaker.limits` which calculates Blaker CI which is not covered here and `propCI` which provides similar functionality.

Other Base methods of CI estimation given x & n: `PlotciAllxg`, `PlotciAllx`, `PlotciEXx`, `ciASx`, `ciAllx`, `ciBAx`, `ciEXx`, `ciLTx`, `ciSCx`, `ciTWx`, `ciWDx`

## Examples

 ```1 2``` ```x=5; n=5; alp=0.05 ciLRx(x,n,alp) ```

### Example output

```  x      LLRx      ULRx LABB UABB ZWI
1 5 0.6810021 0.9999591   NO   NO  NO
```

proportion documentation built on May 1, 2019, 7:54 p.m.