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Microplate library for parsing wet lab data.
There is a newer version: 1.0.4
/**
 * Licensed to the Apache Software Foundation (ASF) under one
 * or more contributor license agreements.  See the NOTICE file
 * distributed with this work for additional information
 * regarding copyright ownership.  The ASF licenses this file
 * to you under the Apache License, Version 2.0 (the
 * "License"); you may not use this file except in compliance
 * with the License.  You may obtain a copy of the License at
 *
 *   http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing,
 * software distributed under the License is distributed on an
 * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
 * KIND, either express or implied.  See the License for the
 * specific language governing permissions and limitations
 * under the License.
 */

/* --------------------------------- Package -------------------------------- */

package com.github.jessemull.microflex.integerflex.stat;

/* ------------------------------ Dependencies ------------------------------ */

import java.util.List;

/**
 * This class calculates the kurtosis of integer plate stacks, plates, 
 * wells and well sets using the following unbiased formula:
 * 
 * 


 * 
 * [n * (n + 1) / (n - 1) * (n - 2) * (n - 3)] * SUMOF(Fourth Moment / (Standard Deviation)^2) where n is the number of values
 * 
 * 


 * 
 * Statistical operations can be performed on stacks, plates, sets and wells using
 * standard or aggregated functions. Standard functions calculate the desired
 * statistic for each well in the stack, plate or set. Aggregated functions aggregate
 * the values from all the wells in the stack, plate or set and perform the statistical
 * operation on the aggregated values. Both standard and aggregated functions can
 * be performed on a subset of data within the stack, plate, set or well.
 * 
 * 


 * 
 * The methods within the MicroFlex library are meant to be flexible and the
 * descriptive statistic object supports operations using a single stack, plate,
 * set or well as well as collections and arrays of stacks, plates, sets or wells. 
 *  
 * 
 *    
 *    
 *    
 *    
 *    
 *       
 *       
 *       
 *       
 *    
 *    
 *       
 *       
 *       
 *       
 *    
 * Operation Beginning
Index Length of
Subset Input/Output

 *          
 *             
 *                
 *             
 *          Standard  
 *       
 *          
 *             
 *                
 *             
 *          +/-  
 *       
 *          
 *             
 *                
 *             
 *          +/-  
 *       
 *          
 *             
 *                
 *             
 *             
 *                
 *             
 *          Accepts a single well, set, plate or stack as input
Calculates the statistic for each well in a well, set, plate or stack  
 *       

 *          
 *             
 *                
 *             
 *          Aggregated  
 *       
 *          
 *             
 *                
 *             
 *          +/-  
 *       
 *          
 *             
 *                
 *             
 *          +/-  
 *       
 *          
 *             
 *                
 *             
 *              
 *                
 *             
 *          Accepts a single well/set/plate/stack or a collection/array of wells/sets/plates/stacks as input
Aggregates the data from all the wells in a well/set/plate/stack and calculates the statistic using the aggregated data  
 *       
 * 
 * @author Jesse L. Mull
 * @update Updated Oct 18, 2016
 * @address http://www.jessemull.com
 * @email [email protected]
 */
public class KurtosisInteger extends DescriptiveStatisticInteger {
	
	/**
     * Calculates the kurtosis.
     * @param    List    the list
     * @return                   the result
     */
	public double calculate(List list) {
	
		if(list.size() <= 3) {
			throw new ArithmeticException("The kurtosis input list must contain " +
					"greater than three arguments.");
		}
		
		double n = list.size();
		double mean = this.mean(list);
		double secondMoment = 0;
		double fourthMoment = 0;

    	for(double db : list) {
    		
    		double second = db - mean;
    		second = Math.pow(second, 2);
    		secondMoment += second;
    		
    		double fourth = db - mean;
    		fourth = Math.pow(fourth, 4);;
    		fourthMoment += fourth;

    	}
		 
    	secondMoment = secondMoment / (n - 1);
    	secondMoment = Math.pow(secondMoment, 2);
    	fourthMoment = fourthMoment / secondMoment;

    	double coefficient =  (n * (n + 1)) / ((n - 1) * (n - 2) * (n - 3));
    	double subtrahend = (3 * Math.pow(n - 1, 2)) / ((n - 2) * (n - 3));
        
    	return fourthMoment * coefficient - subtrahend;
    }
    
    /**
     * Calculates the kurtosis of the values between the beginning and ending 
     * indices.
     * @param    List    the list
     * @param    int             beginning index of subset
     * @param    int             length of subset
     * @return                   the result
     */
    public double  calculate(List list, int begin, int length) {
        return calculate(list.subList(begin, begin + length));
    }

	/**
     * Calculates the mean.
     * @param    List    the list
     * @return                   the result
     */
    private double mean(List list) {
        
        double sum = 0;
        
        for(double db : list) {
            sum += db;
        }
        
        return sum / list.size();
    }
    
}