cumulative_difference_plot: Generate the cumulative difference-plot

In RVCompare: Compare Real Valued Random Variables

Generate the cumulative difference-plot

Description

Generate the cumulative difference-plot given the observed samples using the bootstrap method.

Usage

cumulative_difference_plot(
  X_A_observed,
  X_B_observed,
  isMinimizationProblem,
  labelA = "X_A",
  labelB = "X_B",
  alpha = 0.05,
  EPSILON = 1e-20,
  nOfBootstrapSamples = 1000,
  ignoreMinimumLengthCheck = FALSE
)

Arguments

X_A_observed	array of the observed samples (real values) of X_A.
X_B_observed	array of the observed samples (real values) of X_B, it needs to have the same length as X_A.
isMinimizationProblem	a boolean value where TRUE represents that lower values are preferred to larger values.
labelA	(optional, default value "X_A") the label corresponding to X_A.
labelB	(optional, default value "X_B") the label corresponding to X_B.
alpha	(optional, default value 0.05) the error of the confidence interval. If alpha = 0.05 then we have 95 percent confidence interval.
EPSILON	(optional, default value 1e-20) minimum difference between two values to be considered different.
nOfBootstrapSamples	(optional, default value 1e3) how many bootstrap samples to average. Increases computation time.
ignoreMinimumLengthCheck	(optional, default value FALSE) whether to skip the check for a minimum length of 100 in X_A_observed and X_A_observed.

Value

retunrs and shows the cumulative difference-plot

Examples

### Example 1 ###
X_A_observed <- rnorm(100, mean = 2, sd = 1)
X_B_observed <- rnorm(100, mean = 2.1, sd = 0.5)

 cumulative_difference_plot(X_A_observed, X_B_observed, TRUE, labelA="X_A", labelB="X_B")



### Example 2 ###
# Comparing the optimization algorithms PL-EDA and PL-GS
# with 400 samples each.
PL_EDA_fitness <- c(
52235, 52485, 52542, 52556, 52558, 52520, 52508, 52491, 52474, 52524,
52414, 52428, 52413, 52457, 52437, 52449, 52534, 52531, 52476, 52434,
52492, 52554, 52520, 52500, 52342, 52520, 52392, 52478, 52422, 52469,
52421, 52386, 52373, 52230, 52504, 52445, 52378, 52554, 52475, 52528,
52508, 52222, 52416, 52492, 52538, 52192, 52416, 52213, 52478, 52496,
52444, 52524, 52501, 52495, 52415, 52151, 52440, 52390, 52428, 52438,
52475, 52177, 52512, 52530, 52493, 52424, 52201, 52484, 52389, 52334,
52548, 52560, 52536, 52467, 52392, 51327, 52506, 52473, 52087, 52502,
52533, 52523, 52485, 52535, 52502, 52577, 52508, 52463, 52530, 52507,
52472, 52400, 52511, 52528, 52532, 52526, 52421, 52442, 52532, 52505,
52531, 52644, 52513, 52507, 52444, 52471, 52474, 52426, 52526, 52564,
52512, 52521, 52533, 52511, 52416, 52414, 52425, 52457, 52522, 52508,
52481, 52439, 52402, 52442, 52512, 52377, 52412, 52432, 52506, 52524,
52488, 52494, 52531, 52471, 52616, 52482, 52499, 52386, 52492, 52484,
52537, 52517, 52536, 52449, 52439, 52410, 52417, 52402, 52406, 52217,
52484, 52418, 52550, 52513, 52530, 51667, 52185, 52089, 51853, 52511,
52051, 52584, 52475, 52447, 52390, 52506, 52514, 52452, 52526, 52502,
52422, 52411, 52171, 52437, 52323, 52488, 52546, 52505, 52563, 52457,
52502, 52503, 52126, 52537, 52435, 52419, 52300, 52481, 52419, 52540,
52566, 52547, 52476, 52448, 52474, 52438, 52430, 52363, 52484, 52455,
52420, 52385, 52152, 52505, 52457, 52473, 52503, 52507, 52429, 52513,
52433, 52538, 52416, 52479, 52501, 52485, 52429, 52395, 52503, 52195,
52380, 52487, 52498, 52421, 52137, 52493, 52403, 52511, 52409, 52479,
52400, 52498, 52482, 52440, 52541, 52499, 52476, 52485, 52294, 52408,
52426, 52464, 52535, 52512, 52516, 52531, 52449, 52507, 52485, 52491,
52499, 52414, 52403, 52398, 52548, 52536, 52410, 52549, 52454, 52534,
52468, 52483, 52239, 52502, 52525, 52328, 52467, 52217, 52543, 52391,
52524, 52474, 52509, 52496, 52432, 52532, 52493, 52503, 52508, 52422,
52459, 52477, 52521, 52515, 52469, 52416, 52249, 52537, 52494, 52393,
52057, 52513, 52452, 52458, 52518, 52520, 52524, 52531, 52439, 52530,
52422, 52649, 52481, 52256, 52428, 52425, 52458, 52488, 52502, 52373,
52426, 52441, 52471, 52468, 52465, 52265, 52455, 52501, 52340, 52457,
52275, 52527, 52574, 52474, 52487, 52416, 52634, 52514, 52184, 52430,
52462, 52392, 52529, 52178, 52495, 52438, 52539, 52430, 52459, 52312,
52437, 52637, 52511, 52563, 52270, 52341, 52436, 52515, 52480, 52569,
52490, 52453, 52422, 52443, 52419, 52512, 52447, 52425, 52509, 52180,
52521, 52566, 52060, 52425, 52480, 52454, 52501, 52536, 52143, 52432,
52451, 52548, 52508, 52561, 52515, 52502, 52468, 52373, 52511, 52516,
52195, 52499, 52534, 52453, 52449, 52431, 52473, 52553, 52444, 52459,
52536, 52413, 52537, 52537, 52501, 52425, 52507, 52525, 52452, 52499
)
PL_GS_fitness <- c(
52476, 52211, 52493, 52484, 52499, 52500, 52476, 52483, 52431, 52483,
52515, 52493, 52490, 52464, 52478, 52440, 52482, 52498, 52460, 52219,
52444, 52479, 52498, 52481, 52490, 52470, 52498, 52521, 52452, 52494,
52451, 52429, 52248, 52525, 52513, 52489, 52448, 52157, 52449, 52447,
52476, 52535, 52464, 52453, 52493, 52438, 52489, 52462, 52219, 52223,
52514, 52476, 52495, 52496, 52502, 52538, 52491, 52457, 52471, 52531,
52488, 52441, 52467, 52483, 52476, 52494, 52485, 52507, 52224, 52464,
52503, 52495, 52518, 52490, 52508, 52505, 52214, 52506, 52507, 52207,
52531, 52492, 52515, 52497, 52476, 52490, 52436, 52495, 52437, 52494,
52513, 52483, 52522, 52496, 52196, 52525, 52490, 52506, 52498, 52250,
52524, 52469, 52497, 52519, 52437, 52481, 52237, 52436, 52508, 52518,
52490, 52501, 52508, 52476, 52520, 52435, 52463, 52481, 52486, 52489,
52482, 52496, 52499, 52443, 52497, 52464, 52514, 52476, 52498, 52496,
52498, 52530, 52203, 52482, 52441, 52493, 52532, 52518, 52474, 52498,
52512, 52226, 52538, 52477, 52508, 52243, 52533, 52463, 52440, 52246,
52209, 52488, 52530, 52195, 52487, 52494, 52508, 52505, 52444, 52515,
52499, 52428, 52498, 52244, 52520, 52463, 52187, 52484, 52517, 52504,
52511, 52530, 52519, 52514, 52532, 52203, 52485, 52439, 52496, 52443,
52503, 52520, 52516, 52478, 52473, 52505, 52480, 52196, 52492, 52527,
52490, 52493, 52252, 52470, 52493, 52533, 52506, 52496, 52519, 52492,
52509, 52530, 52213, 52499, 52492, 52528, 52499, 52526, 52521, 52488,
52485, 52502, 52515, 52470, 52207, 52494, 52527, 52442, 52200, 52485,
52489, 52499, 52488, 52486, 52232, 52477, 52485, 52490, 52524, 52470,
52504, 52501, 52497, 52489, 52152, 52527, 52487, 52501, 52504, 52494,
52484, 52213, 52449, 52490, 52525, 52476, 52540, 52463, 52200, 52471,
52479, 52504, 52526, 52533, 52473, 52475, 52518, 52507, 52500, 52499,
52512, 52478, 52523, 52453, 52488, 52523, 52240, 52505, 52532, 52504,
52444, 52194, 52514, 52474, 52473, 52526, 52437, 52536, 52491, 52523,
52529, 52535, 52453, 52522, 52519, 52446, 52500, 52490, 52459, 52467,
52456, 52490, 52521, 52484, 52508, 52451, 52231, 52488, 52485, 52215,
52493, 52475, 52474, 52508, 52524, 52477, 52514, 52452, 52491, 52473,
52441, 52520, 52471, 52466, 52475, 52439, 52483, 52491, 52204, 52500,
52488, 52489, 52519, 52495, 52448, 52453, 52466, 52462, 52489, 52471,
52484, 52483, 52501, 52486, 52494, 52473, 52481, 52502, 52516, 52223,
52490, 52447, 52222, 52469, 52509, 52194, 52490, 52484, 52446, 52487,
52476, 52509, 52496, 52459, 52474, 52501, 52516, 52223, 52487, 52468,
52534, 52522, 52474, 52227, 52450, 52506, 52193, 52429, 52496, 52493,
52493, 52488, 52190, 52509, 52434, 52469, 52510, 52481, 52520, 52504,
52230, 52500, 52487, 52517, 52473, 52488, 52450, 52203, 52215, 52490,
52479, 52515, 52210, 52485, 52516, 52504, 52521, 52499, 52503, 52526)
# Considering that the LOP is a maximization problem, we need isMinimizationProblem=FALSE.

 cumulative_difference_plot(PL_EDA_fitness,
                            PL_GS_fitness,
                            isMinimizationProblem=FALSE,
                            labelA="PL-EDA",
                            labelB="PL-GS")

RVCompare documentation built on Aug. 21, 2023, 5:13 p.m.