Simultaneous CIs for Ratios of Means of Log-Normal Populations with Zeros

## Project description     ## LN0SCIs

Jing Xu, Xinmin Li, Hua Liang

### Introduction

This Python package based on the paper of Simultaneous Confidence Intervals for Ratios of Means of Log-normal Populations with Zeros by Xu et al. It provides some methods for construct simultaneous confidence intervals for ratios of means of Log-normal populations with excess zeros. At last, we select 4 excellent methods which based on generalized pivotal quantity with order statistics and two-step MOVER intervals. For the convenience of use, we make a Python package called LN0SCIs, and it also has a R version package on CRAN: https://CRAN.R-project.org/package=LN0SCIs

• If you are a R User, you can install in your R kernal by Github:
• devtools::install_github(‘DataXujing/LN0SCIs’)
• Or you can also install by CRAN:
• install.packages(‘LN0SCIs’)
• If you are a Python user, you can
• pip install LN0SCIs

### Methods

We provaide four main functions in our LN0SCIs packages, FGW(),FGH(),MOVERW() and MOVERH(), if you want to deep understanding these four methods, you can read our paper: Simultaneous Confidence Intervals for Ratios of Means of Log-normal Populations with Zeros. the code we trust in GitHub. If you want to know how to realize them, you can read the source code.

### Examples

• FGW()
```from LN0SCIs import *
#Example1:
alpha = 0.05
p = np.array([0.2,0.2,0.2])
n = np.array([30,30,30])
mu = np.array([0,0,0])
sigma = np.array([1,1,1])
N = 1000
FGW(n,p,mu,sigma,N)
#Example2:
p = np.array([0.1,0.1,0.1,0.1])
n = np.array([30,30,30,30])
mu = np.array([0,0,0,0])
sigma = np.array([1,1,1,1])
C2 = np.array([[-1,1,0,0],[-1,0,1,0],[-1,0,0,1],[0,-1,1,0],[0,-1,0,1],[0,0,-1,1]])
N = 1000
FGW(n,p,mu,sigma,N,C2 = C2)
```
```====================Method: FGW=====================
The Simultaneous Confidence Intervals are:
The1th CIs            The2th CIs            The3th CIs
0  【-0.843638,0.789044】  【-0.629208,1.075959】  【-0.604469,1.158544】
**********************Time**************************
The cost time is:0 secs
====================Method: FGW=====================
The Simultaneous Confidence Intervals are:
The1th CIs           The2th CIs           The3th CIs  \
0  【-0.912169,1.578679】  【-1.02404,0.812882】  【-0.83778,1.382352】

The4th CIs            The5th CIs           The6th CIs
0  【-1.597962,0.650222】  【-1.337939,1.203199】  【-0.546039,1.25945】
**********************Time**************************
The cost time is:0 secs
```
• FGH()
```alpha = 0.05
p = np.array([0.2,0.2,0.2])
n = np.array([30,30,30])
mu = np.array([0,0,0])
sigma = np.array([1,1,1])
N = 1000
FGH(n,p,mu,sigma,N)
#Example2:
p = np.array([0.1,0.1,0.1,0.1])
n = np.array([30,30,30,30])
mu = np.array([0,0,0,0])
sigma = np.array([1,1,1,1])
C2 = np.array([[-1,1,0,0],[-1,0,1,0],[-1,0,0,1],[0,-1,1,0],[0,-1,0,1],[0,0,-1,1]])
N = 1000
FGH(n,p,mu,sigma,N,C2 = C2)
```
```====================Method: FGH=====================
The Simultaneous Confidence Intervals are:
The1th CIs            The2th CIs            The3th CIs
0  【-0.992276,1.455247】  【-0.703231,1.372774】  【-1.005873,1.124758】
**********************Time**************************
The cost time is:0 secs
====================Method: FGH=====================
The Simultaneous Confidence Intervals are:
The1th CIs            The2th CIs            The3th CIs  \
0  【-1.62426,0.624984】  【-1.514528,0.553936】  【-1.565943,0.911157】

The4th CIs            The5th CIs           The6th CIs
0  【-0.66646,1.010746】  【-0.829753,1.269381】  【-0.762683,1.07889】
**********************Time**************************
The cost time is:0 secs
```
• MOVERW()
```alpha = 0.05
p = np.array([0.2,0.2,0.2])
n = np.array([30,30,30])
mu = np.array([0,0,0])
sigma = np.array([1,1,1])
N = 1000
MOVERW(n,p,mu,sigma,N)
#Example2:
p = np.array([0.1,0.1,0.1,0.1])
n = np.array([30,30,30,30])
mu = np.array([0,0,0,0])
sigma = np.array([1,1,1,1])
C2 = np.array([[-1,1,0,0],[-1,0,1,0],[-1,0,0,1],[0,-1,1,0],[0,-1,0,1],[0,0,-1,1]])
N = 1000
MOVERW(n,p,mu,sigma,N,C2 = C2)
```
```====================Method: FGH=====================
The Simultaneous Confidence Intervals are:
The1th CIs            The2th CIs            The3th CIs
0  【-1.103496,1.211033】  【-1.030952,0.888781】  【-1.314926,1.059975】
**********************Time**************************
The cost time is:0 secs
====================Method: FGH=====================
The Simultaneous Confidence Intervals are:
The1th CIs            The2th CIs            The3th CIs  \
0  【-1.68825,0.349316】  【-1.270833,1.236153】  【-1.304731,1.053776】

The4th CIs            The5th CIs            The6th CIs
0  【-0.349427,1.679719】  【-0.364992,1.484843】  【-1.294225,1.071433】
**********************Time**************************
The cost time is:0 secs
```
• MOVERH()
```alpha = 0.05
p = np.array([0.2,0.2,0.2])
n = np.array([30,30,30])
mu = np.array([0,0,0])
sigma = np.array([1,1,1])
N = 1000
MOVERH(n,p,mu,sigma,N)
#Example2:
p = np.array([0.1,0.1,0.1,0.1])
n = np.array([30,30,30,30])
mu = np.array([0,0,0,0])
sigma = np.array([1,1,1,1])
C2 = np.array([[-1,1,0,0],[-1,0,1,0],[-1,0,0,1],[0,-1,1,0],[0,-1,0,1],[0,0,-1,1]])
N = 1000
MOVERH(n,p,mu,sigma,N,C2 = C2)
```
```====================Method: FGH=====================
The Simultaneous Confidence Intervals are:
The1th CIs            The2th CIs          The3th CIs
0  【-1.013305,0.765726】  【-1.152934,0.823283】  【-0.914194,0.8239】
**********************Time**************************
The cost time is:0 secs
====================Method: FGH=====================
The Simultaneous Confidence Intervals are:
The1th CIs            The2th CIs           The3th CIs  \
0  【-0.681666,1.693927】  【-0.750657,1.458978】  【-1.21012,0.855608】

The4th CIs            The5th CIs            The6th CIs
0  【-1.302431,1.003355】  【-1.762379,0.407925】  【-1.527028,0.467458】
**********************Time**************************
The cost time is:0 secs
```

### Supports

Tested on Python 2.7, 3.5, 3.6

you can log in Xujing’s home page: https://dataxujing.coding.me or https://dataxujing.github.io to find the author(s), and if you want to learn more about simultaneous confidence intervals for the mixture distribution, you shou read the paper: Simulataneous Confidence Intervals for ratios of Means of Log-normal Populations with Zeros, which written by Jing Xu, Xinmin Li, and Hua Liang.

## Project details

This version 0.1.2 0.1.1 0.1.0