The world saw its first case of the Covid19 virus in Wuhan, China in late 2019. This virus gives rise to a global pandemic from which the world is still recovering from. The virus contributed to a significant increase in deaths worldwide, destruction of families through emotional trauma, the loss of many jobs, a massive increase in the cost of living and major disruption in the education system. According to the World Health Organization (WHO), Corona virus disease (Covid19) is an infectious disease caused by the SARSCoV2 virus.
The Corona virus disease (Covid19) has led to a high mortality rate globally, triggering an unprecedented public health crisis. On March 11, 2020, the World Health Organization declared Covid19 as a global pandemic
The Covid19 disease has expanded worldwide, producing over 315 million cases and 5.5 million deaths reported by the World Health Organization (WHO). There have been about 46000 confirmed cases in Guyana as of January 14, 2022, with over 1070 deaths. The WHO has termed this current epidemic a global emergency and it is a public health responsibility on a massive scale.
The time between the commencement of symptomatic manifestation and death is approximately 28 weeks. In addition, most countries including Guyana have implemented 14 days quarantine upon testing positive. The Government of Guyana introduced a lockdown to suppress the rate of transmission of this deadly virus.
Mathematical modeling has been generating quantitative information for a while in epidemiology and providing useful guidelines for outbreak management and policy development
Transmuted distributions have an additional parameter that gives the flexibility of capturing any skewness in the data. As a result, a number of new distributions have been developed to model realworld data. Additionally, a number of researchers successfully fitted different Transmuted distributions to the Covid19 data of various countries. The Odd lomaxG inverse Weibull distribution
In this study, the Transmuted Weibull distribution is used to model the Covid19 data of Guyana from the period of March 1 2020 to November 30 2021. The model parameters are estimated by the method of maximum likelihood estimators by analyzing the Covid19 cumulative deaths of Guyana. In addition, the properties and characterization of the model is included in the study.
A random variable X is said to have a Weibull distribution with parameters η > 0 and σ > 0 if its probability density function (pdf) is given by
The cumulative distribution function of X is given by
Using equation 2, we can obtain the CDF of the transmuted Weibull distribution.
Where
Differentiating equation 3 with respect to x, given by
After differentiating the above equation with respect to x, the pdf of the Transmuted Weibull distribution with parameters η, σ and λ is
The expected value of the
Thus, the
After solving the above equation,
The reliability function of the transmuted Weibull distribution is
By the method of inversion, random numbers from the Transmuted Weibull distribution can be generated as:
Where
Setting
The variance of the Transmuted Weibull distribution is given as:
The standard deviation of the Transmuted Weibull distribution is given as:
The parameters of the Transmuted Weibull distribution are estimated using the maximum likelihood method.
Let
and the loglikelihood function
Differentiating equation 14, with respect to
The maximum likelihood of the parameters are performed in the Mathematica software since it has a ‘FindMaximum’ function.
A simulation study is carried out in order to test the efficiency of the estimation methods. The random sample sizes of n= 25, 75 and 175 are generated from the transmuted Weibull distribution with parameters η, λ and σ. The values of the parameters are chosen as η=0.6, λ =0.7 and σ= 0.9. For each combination of η, λ and σ and n there are 200 replications. The parameters are estimated using the maximum likelihood estimates. The values of the mean, Bias and RSME (Root mean square error) are obtained and the results are presented in







0.6619 
0.0619 
0.0311 
25 

0.6346 
0.1154 
0.2664 


0.8486 
0.0514 
0.1161 


0.6845 
0.0845 
0.0376 
75 

0.6031 
0.1469 
0.2063 


0.7952 
0.1048 
0.1239 


0.7071 
0.1071 
0.0439 
175 

0.5424 
0.2076 
0.1908 


0.7502 
0.1498 
0.0872 
From
The Covid19 data is from Guyana and it covers a period of 628 days, from March12, 2020 to November 30, 2021.
The data is presented using the daily new deaths (ND), the daily cumulative deaths (CD) and the daily cumulative cases (CC) and calculated as follows:
Data points that have no new deaths are excluded from the data analysis.
.0158 .0158 .0469 .6234 .6184 .5724 .0161 .0159 .0317 .0158 .9833 .9465 .9225 .4050 .8323 .7806 .7843 .7236 .3751 .7297 .7348 .6993 .6944 .8019 .6392 .9404 .6464 .9096 .9188 .6088 .5974 .2916 .2884 .5713 .2822 .5499 .5430 .8086 .5283 .2641 .5088 .8666 .2461 .4847 .4833 .4683 .6842 .2285 .2274 .4379 .2190 .2122 .2099 .4172 .2043 .5969 .1970 .3872 .1900 .1893 .3611 .1794 .1723 .1721 .3390 .1681 .1639 .3259 .3262 .3209 .1572 .3108 .1555 .2778 .2763 .1354 .1341 .1335 .2560 .1280 .1269 .1256 .2503 .2488 .2469 .1223 .1207 .2419 .3608 .2379 .2362 .1168 .1157 .2321 .1153 .1136 .1130 .1112 .1101 .1087





397 
0.1997 
0.0156 
0.9833 
1.979 
The Covid19 data is fitted into the transmuted Weibull distribution, the 2parameter Weibull distribution, with CDF:
and the 3parameter Weibull distribution with CDF:
.
The best mathematical model for fitting the Covid19 data of Guyana is assessed using the Akaike Information Criterion (AIC) approach and is presented in
where k is the number of parameters in the model. The model with the smallest AIC value is an indication that the model fits the Covid19 data well.












2parameter Weibull 
1.145 

0.210 
248.742 
493.484 
3parameter Weibull 
0.900 
0.100 
0.700 
42.817 
91.634 
Transmuted Weibull 
1.242 
0.610 
0.286 
254.066 
502.132 
In
The results obtained using the Transmuted Weibull distribution, 2parameter Weibull and 3parameter Weibull distribution indicates that the transmuted Weibull distribution fit the Covid19 data of Guyana well since it produce the lowest AIC value while the 3parameter Weibull distribution had the highest AIC value.
Several Transmuted distributions are used to model the Covid19 data of various countries. Furthermore, these distributions were used to model the Covid19 data of France, United Kingdom and Canada. The goodness of fit of these distributions were assessed using the loglikelihood, Akaike’s Information Criterion (AIC), Bayesian Information Criterion (BIC) and the Kolmogorov Smirnov test for the models. The fit of these distributions were compared with other competitive models.
To date, the transmuted distributions are considered to be the best model for modeling Covid19 data because of its additional parameter which captures any skewness in the data. Also, the transmuted Weibull distribution was not used to model the Covid19 data of any country that was reported in literature. The results produced better results since this particular transmuted distribution was fitted into the Covid19 data of Guyana formed by the daily cumulative deaths from the period of March 12^{th}, 2020 to November 30^{th}, 2021.
Based on this study, the properties and characterization of the transmuted Weibull distribution was examined in detail. The transmuted Weibull distribution was successfully applied to model the Covid19 data of Guyana. The best model for fitting the data was selected using the AIC approach. The results indicated that the 3parameter Weibull had highest AIC value (91.634) while the transmuted Weibull distribution produces the lowest AIC value (502.132). Therefore, based on the findings of this study, the deaths were high and as the vaccine progresses the number of deaths decreased and it was evident in the model. In Guyana, no work has been done using the cumulative deaths and the transmuted Weibull distribution.