weibull4: non-linear regression data fitter to the 4-parameters Weibull...

In weibull4: Fits Data into 4-Parameters Weibull Distribution

Description

Input script for using the weibull4 module. Weibull4 fit data from daily new cases and deaths of an epidemic peak. It was firstly designed to model data from COVID-19

Usage

weibull4(x, y, shape=NA, scale=NA, loc=NA, area=NA, shape2=NA, scale2=NA, loc2=NA,
area2=NA, iter=1000, xmax=0, modes=1, modes2=1, split=NA)

Arguments

x	Vector: time data (may be date/time or numeric)
y	Vector: observed/measure event
shape	Starting value for Weibull's shape parameters. If it is NA, weibull4.fit will try to calculate it from x and y data.
scale	Starting value for Weibull's scale parameters. If it is NA, weibull4.fit will try to calculate it from x and y data.
loc	Starting value for Weibull's location parameters. If it is NA, weibull4.fit will try to calculate it from x and y data.
area	Starting value for Weibull's area parameters or the area under the PDF curve. If it is NA, weibull4.fit will try to calculate it from x and y data.
shape2	Starting value for the shape parameters of the second mode of the Weibull's distribution. If it is NA, weibull4.fit will try to calculate it from x and y data. It works only if modes=2.
scale2	Starting value for the scale parameters of the second mode of the Weibull's distribution. If it is NA, weibull4.fit will try to calculate it from x and y data. It works only if modes=2.
loc2	Starting value for the location parameters of the second mode of the Weibull's distribution. If it is NA, weibull4.fit will try to calculate it from x and y data. It works only if modes=2.
area2	Starting value for the area parameters of the second mode of the Weibull's distribution. If it is NA, weibull4.fit will try to calculate it from x and y data. It works only if modes=2.
iter	Number of iterations to perform Metropolis-MCMC.
split	The date (x axis) in which the data will be split to be calculated by two distinct distribution. This option was implemented to fit data feom the second wave of infections and deaths for COVID-19. With split set, it is possible to analyze curve pattern with up to 4 waves of infection, since both modes and modes2 are set to 2. In this case, the data will be analyzed as two bimodal Weibull distribution.
modes	Sets whether data defore the split date (if the split is not NA) may be fit with unimodal or bimodal Weibull distribution. If split is not set, modes is the number of modes of the unique distribution to be used. This option was implemented to fit data feom the second wave of infections and deaths for COVID-19. Use modes=1 for unimodal distribution (single peak) and modes=2 for bimodal distribution (two peaks, with no or small valley between them).
modes2	Sets whether data after the split date (if split is not NA) may be fit with unimodal or bimodal Weibull distribution. If split is not set, modes2 will not be used. This option was implemented to fit data feom the second wave of infections and deaths for COVID-19. Use modes=1 for unimodal distribution (single peak) and modes=2 for bimodal distribution (two peaks).
xmax	Forecast date to be calculated after x data. It must be in the same format than x.

Details

This package was specially built to fit COVID-19 data on the number of daily new cases and deaths in countries. So x must be integer. Alternatively, Date format is allowed

Value

LIST containning:

Fit data	Matrix with x and y fitted data
Estimates	Matrix containning shape, scale, location, area and SD of the MEtropolis-MCMC in the row 1; and standard deviation for each parameter in the row 2
Markov chains	Matrix containning the Markov chains for shape, scale, location, area and SD parameters

Warning

This package is a secondary product of the reffered science paper. Please, note that there is no warrants or professional support on its use

Note

Comments, suggestions and doubts must be sent to [e-mail]

Author(s)

Vitor Hugo Moreau, Ph.D.

References

MOREAU, V. H. (2021) Using the Weibull distribution to model COVID-19 epidemic data, Model Assisted Statistic Applications, in press.

Examples

## Perform non-linear curve fitting with US' data for daily new deaths of COVID-19, with split date
## on Aug, 15th, bimodal distribution before and unimodal distribution after the split date.
## Examples below are with low number of iterations (1000), because of CRAN rules limitations.
## They will possibily give poor results. For best results set iter=10000.
fit <- weibull4(US_COVID$date, US_COVID$new_deaths, split=as.Date("2020-09-15"),
modes=2, modes2=1,iter=1000)
plot(US_COVID$date, US_COVID$new_deaths, ylab="US' daily new deaths", xlab="Date")
lines(fit[[1]][,1], fit[[1]][,2], col="red")
## Perform non-linear curve fitting with Canada's data for daily new cases of COVID-19 using two
## unimodal Weibull distribution, with split date on Aug,  1st
fit <- weibull4(Canada_COVID$date, Canada_COVID$new_cases, split=as.Date("2020-08-01"),
modes=1, modes2=1, iter=1000)
plot(Canada_COVID$date, Canada_COVID$new_cases, ylab="Canada's daily new cases", xlab="Date")
lines(fit[[1]][,1], fit[[1]][,2], col="red")
## Perform non-linear curve fitting with Brazil's data for daily new deaths of COVID-19 using a
## single bimodal Weibull distribution
fit <- weibull4(Brazil_COVID$date, Brazil_COVID$new_deaths, modes=2, iter=1000)
plot(Brazil_COVID$date, Brazil_COVID$new_deaths, ylab="Brazil's daily new deaths", xlab="Date")
lines(fit[[1]][,1], fit[[1]][,2], col="red")

weibull4 documentation built on Jan. 26, 2021, 1:06 a.m.