distributionH-class {HistDAWass}

Class distributionH.

Description

Class "distributionH" desfines an histogram object The class describes a histogram by means of its cumulative distribution function. The methods are develoved accordingly to the L2 Wasserstein distance between distributions.

A histogram object can be created also with the function distributionH(...), the costructor function for creating an object containing the description of a histogram.

Usage

## S4 method for signature 'distributionH'
initialize(
  .Object,
  x = numeric(0),
  p = numeric(0),
  m = numeric(0),
  s = numeric(0)
)

distributionH(x = numeric(0), p = numeric(0))

Arguments

.Object

the type ("distributionH")

x

a numeric vector. it is the domain of the distribution (i.e. the extremes of bins).

p

a numeric vector (of the same lenght of x). It is the cumulative distribution function CDF.

m

(optional) a numeric value. Is the mean of the histogram.

s

(optional) a numeric positive value. It is the standard deviation of a histogram.

Details

Class distributionH defines a histogram object

Value

A distributionH object

Objects from the Class

Objects can be created by calls of the form new("distributionH", x, p, m, s).

Author(s)

Antonio Irpino

References

Irpino, A., Verde, R. (2015) Basic statistics for distributional symbolic variables: a new metric-based approach Advances in Data Analysis and Classification, DOI 10.1007/s11634-014-0176-4

See Also

meanH computes the mean. stdH computes the standard deviation.

Examples

#---- initialize a distributionH object mydist
# from a simple histogram
# ----------------------------
# | Bins    |  Prob  | cdf   |
# ----------------------------
# | [1,2)   |  0.4   | 0.4   |
# | [2,3]   |  0.6   | 1.0   |
# ----------------------------
# | Tot.    |  1.0   | -     |
# ----------------------------
mydist <- new("distributionH", c(1, 2, 3), c(0, 0.4, 1))
str(mydist)
# OUTPUT
# Formal class 'distributionH' [package "HistDAWass"] with 4 slots
#   ..@ x: num [1:3] 1 2 3 the quantiles
#   ..@ p: num [1:3] 0 0.4 1 the cdf
#   ..@ m: num 2.1 the mean
#   ..@ s: num 0.569 the standard deviation
# or using
mydist <- distributionH(x = c(1, 2, 3), p = c(0, 0.4, 1))