distributionH-class: Class distributionH. In HistDAWass: Histogram-Valued Data Analysis

Description

Class distributionH.

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

 ```1 2 3 4 5``` ```## 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)`.

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

`meanH` computes the mean. `stdH` computes the standard deviation.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ``` #---- 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)) ```