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/**
* 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.microflexbigdecimal.stat;
/* ------------------------------ Dependencies ------------------------------ */
import java.math.BigDecimal;
import java.math.MathContext;
import java.util.List;
/**
* This class calculates the kurtosis of BigDecimal 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 Kurtosis extends DescriptiveStatisticContext {
/**
* Calculates the kurtosis.
* @param List the list
* @return the result
*/
public BigDecimal calculate(List list, MathContext mc) {
if(list.size() <= 3) {
throw new ArithmeticException("The kurtosis input list must contain " +
"greater than three arguments.");
}
BigDecimal length = new BigDecimal(list.size() + "", mc);
BigDecimal mean = this.mean(list, mc);
BigDecimal secondMoment = new BigDecimal("0", mc);
BigDecimal fourthMoment = new BigDecimal("0", mc);
for(BigDecimal bd : list) {
BigDecimal second = bd.subtract(mean, mc);
second = second.pow(2, mc);
secondMoment = secondMoment.add(second, mc);
BigDecimal fourth = bd.subtract(mean, mc);
fourth = fourth.pow(4, mc);
fourthMoment = fourthMoment.add(fourth, mc);
}
secondMoment = secondMoment.divide(length.subtract(BigDecimal.ONE, mc), mc);
secondMoment = secondMoment.pow(2, mc);
fourthMoment = fourthMoment.divide(secondMoment, mc);
double n = length.doubleValue();
double coefficientDouble = (n * (n + 1)) / ((n - 1) * (n - 2) * (n - 3));
double subtrahendDouble = (3 * Math.pow(n - 1, 2)) / ((n - 2) * (n - 3));
BigDecimal coefficient = new BigDecimal(coefficientDouble + "", mc);
BigDecimal subtrahend = new BigDecimal(subtrahendDouble + "", mc);
return fourthMoment.multiply(coefficient).subtract(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 BigDecimal calculate(List list, int begin, int length, MathContext mc) {
return calculate(list.subList(begin, begin + length), mc);
}
/**
* Calculates the mean.
* @param List the list
* @return the result
*/
private BigDecimal mean(List list, MathContext mc) {
BigDecimal sum = BigDecimal.ZERO;
for(BigDecimal db : list) {
sum = sum.add(db);
}
return sum.divide(BigDecimal.valueOf(list.size()), mc);
}
}
