weibull4 (version 1.0.0)

weibull4.fit: Weibull 4-parameters Metropolis-MCMC non-linear curve fitting function

Description

Package to perform non-linear regression in data on the number of daily new cases and daily new deaths of COVID-19 and other epidemics to the 4-parameters Weibull distribution using Metropolis-Markov Chain-Monte Carlo Simulations (MCMC), as described in Moreau, 2021

Usage

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

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.

modes

Sets whether data may be fit with unimodal or bimodal Weibull distribution. 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.

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

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

References

MOREAU, V. H. (2021) Forecast projections of COVID-19 pandemic by Weibull distribution from daily new cases and deaths data, Model Assisted Statistics and Applications. in press. Part of the MCMC code came from the Florian Hartig blog: "https://theoreticalecology.wordpress.com/2010/09/17/metropolis-hastings-mcmc-in-r/"

Examples

# NOT RUN {
## Perform non-linear curve fitting with World's data for daily new deaths
## of COVID-19
## 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, 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, modes=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")
# }