Cumulative Normal Distribution and Compound Growth Rate for India on 06.06.2020

Cumulative Normal Distribution and Compound Growth Rate for India on 06.06.2020

 

Dr Himanshu Shekhar

 

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Introduction: In a constant effort to understand the behaviour of cumulative confirmed cases and related parameters, many new terms are explored, calculated and presented. That included growth factor, doubling period, exponential variation, normal distribution, turnaround, number of test per case etc. In the present post, attempt is made to analyse two terms for India, Maharashtra and Delhi – Cumulative Normal Distribution and Compound growth rate.

Mathematical Treatment: The cumulative normal distribution is obtained in mathematics by integrating the normal distribution curve and is representative of cumulative frequency distribution. It has an S-shaped curve having three separate zones: initial slow rise zone with increasing rate of growth, zone of point of inflexion and reducing rate of growth and zone of very insignificant rise or flat portion. As the data in case of current situation is obtained on daily basis, the integration is although possible but is incorrect way to represent the discrete datasets. This post gives variation of cumulative normal distribution against actual cumulative confirmed cases on 06.06.2020.

As far as compound growth rate of confirmed cases is concerned, it is similar to compound interest calculation. It is the rate at which if the cases grow, the required doubling period is achieved. As a thumb rule, it is calculated as 72 divided by doubling period. But in the post, it is calculated by using the formula, 2 = (1+r)^DP, where DP = doubling period in days and r = compound growth rate in percentage. This post gives variation, of compound growth rate, as presented in some of the media and reports. Although compound growth rate can be calculated on daily, 2-day, 3-day or 7-day basis, also.

India Maharashtra and Delhi: The value of salient parameters for the three geographical entities are given below:

 

Parameters on 06.06.2020	India	Maharashtra	Delhi
Cumulative Confirmed Cases	236657	80229	26334
One day confirmed cases	9887	2436	1330
Growth Factor on	1.0036	0.8305	0.97866
Doubling Period, days	16	16	13

For India, the cumulative normal distribution curve, along with actual cumulative confirmed cases till 06.06.2020, is plotted below. The variation is more or less matching till available data. However, the actual are slightly on upper side, indicating a chance of more upward deviation, in confirmed cases.

 

Similarly, the compound growth rate in percentage is also calculated and given for India, below.

 

For Maharashtra also, the cumulative normal distribution curve, superimposed on actual confirmed cases is generated. The compound growth rate is also calculated and variation is displayed, which indicates a continuous reduction in numerical values.

For Delhi also, the cumulative normal distribution curve is generated and also the compound growth rate curves. The values are although nicely matching till 06.06.2020, but some control is needed for quick turnaround.

 

Conclusion: The cumulative normal distribution curve is plotted against actual total confirmed cases till 06.06.2020. The curve is matching till available data for all three cases, namely India, Maharashtra and Delhi. Hope that turnaround, as predicted is achieved. The compound growth rate is calculated, after looking at some of the media reports and the same has downward trend for Indian and Maharashtra, but it is rising for Delhi. The value is between around 5%.

 

Dr Himanshu Shekhar