Bill Adongo Profile(2007-2009)

ADONGO’S PERIODIC STATISTICS

INTRODUCTION

In every day activities we use observations of events that happened in the past to forecast future events or costs. For example, data that was collected over several years about the average event or cost may be used to estimate the expected event or cost in future years.

This help as to prevent losses, risks, or contingencies that are likely to occur in the future years to come.

A country which is aware of her future consequences or risks has a high chance of managing her resources, since she will be able to find ways of controlling or preventing such risks.

In fact, for the interest of knowledge contribution, I have had come out with a concept called periodic statistics. This particular concept will help us to estimate or predict futures events.

ADONGO’S PERIODIC OCCURENCES

At K^th period for relative occurrence of x_k and y_k. Where x_k and y_k are class occurrence and successful occurrence in class respectively then the formulae for K^th occurrences are given as follow.

   ADONGO’S PERIODIC MEAN

The main aim of the periodic distribution is to use data for prediction and making future decision.

The most common and most effective numerical measures of the centre of a set of data along the K^th period is the Mean. It is the arithmetic average of the values along the K^th period of sample size n+k-1.

The formulae for the periodic Mean which is the relative occurrences of the ramdom variable x_k and y_k are given as,

ADONGO’S PERIODIC VARIANCE

We need a more accurate method for measuring the amount of variation, dispersion or consistency along K^th period of sample size n+k-2 of the data which takes into account the effect of all the data entries.

First, we must agree on what we mean by periodic variation in data. We interpret periodic variation as measuring how each period data values is from the K^th Mean. The Adongo’s variance is given as;

ADONGO’S PERIODIC PROBABILITY

In most areas of human endeavor, there is always an element of uncertainty. If we consider the weather, a stock transaction, or a matter relating on health, we are always face with a certain degree of risks.

In fact, the only things in life that are certain are death and taxes. Therefore, we must be able to assess the degree of uncertainty in any given situation, and this is done mathematically by using Adongo’s periodic probability.

ADONGO’S PERIODIC NORMALCY

PROPERTIES;-

1) It is central at the periodic Mean and

2) It symmetric about the periodic mean.

3) Approximately 68% of a normal sample population along the K^th period lies within the periodic standard deviation of the mean.

4) Approximately 95% of a normal sample lies with two periodic standard deviation of means.

5) The total area under the periodic normally curves one(1).

6) or is precisely equal to the area under the normal curve between x_L and x_R or y_L and y_R and respectively.

Hence, the periodic normal distribution formulae are given as;

CENTRAL PERIODIC LIMIT THEOREM

Consider the distribution of sample periodic means have mean and standard deviation or mean and standard division base on the K^th periodic random samples of size n+k-1 along the period from an underlying periodic population having mean and standard deviation or mean and standard deviation along the K^th period of sample size n+k-1.

The K^th sample standard deviations are given as follow!

If we sample from a normal population along the K^th periods, then the distribution of sample means will be normally distributed periodically also. If we sample from no normal periodic population, then the distribution or the periodic means is approximately

normal if the sample size n+k-1 is large enough (i.e. n+k-1>29).the Z_xk and Z_yk values are calculated as

ADONGO’S MULTI- COMBINATIONAL THEOREM

THEOREM;

For a known variable x_i-1 for generation prediction of the variable x_i(where i = 1,2,3,4…) with a gradient a_i and intercept b_i, then the generation equation is given as,Xi =
Where a_i and b_i are calculated as;

USING ADONGO’S MULTI- COMBINATIONAL THEOREM TO DETERMINE THE CORRELATION COEFFICIENT AMONG THREE OR MORE VARIABLES.

The correlation coefficient is determine from equation Xi = . we use the correlation coefficient to measure the degree of relationship between two or more quantities, let and represent the respective means of the x_i-1 and Xi values from the sample data. The correlation coefficient Ri is then defined as

AIM OF THE THEOREM

To enhance an easy and accurate way for predicting three or more variables when one variable is known .It is use to determine the correlation coefficient among variables.

IMPORTANCE OF THE THEOREM

The theorem is of great important to actuaries, statisticians, economists and many others.

ADONGO’S POINT VALUES INTERVAL THEOREM OF A STRAIGHT LINE EQUATION

If aЄA andbЄB, where “A” contains the possible values of “a" and "B" contains the possible values of  "b". if “A” is a corresponding pair of “B” and “a” is a corresponding pair of “b”, thus we have

INTERCEPT OF A LINE

In fact, with point values theorem, we can determine the intercept of line on a graph as

a-a is a corresponding pair of b+b and a + a is a corresponding pair of b-b.

APPLICATIONS OF PVI THEOREM

Very applicable in statistics, economics, applied sciences, engineering sciences, and actuarial science and is used to draw a line of best fit as long a straight lines graphs are concerned.

Helps to determine the intercept of the axial coordinates x and y.

ADONGO DISTRIBUTION

Consider that the possible outcomes of a given time period or space n can be divided into two categories; those that cause a given event to occur in a particular time or space and those that do not. (i.e. ).

Consider the probability distribution of a time or a space event that occure randomly but has uniform probability of occurrences and if n denote as time or space and Xi denote as the number of times the event occur at a particular time or space. The probability which follows above characteristics is Adongo probability distribution.

MEAN

Given Adongo distribution of successful outcome in time or space N for X times occurrences of the event. The mean of the distribution is given as;

VARIANCE

Given Adongo distribution of successful outcomes and failure in time space N for X times occurrences of the event. The variance of the distribution is given as;

Var(x) =

CHARACTERISTICS OF ADONGO DISTRIBUTION

1. There are exactly two possible outcomes in a given time or space. We can think of these two outcome as “success” and “failure”
2. The probability of certain number of success during a given interval of times or space is determine.
3. The individual success are independent of one another
4. The success will occur uniformly over the entire time or space under consideration.

EXAMPLE

A firm manufacture long rolls of tape and then cuts the rolls into 1200-ft lengths

Extensive measurement have shown that defects in the roll occurs at random with probability 0.40

a. What is the probability that a tape has at most 4 defects?

b. What is the probability that a tape has more than 2 defects?

c. If a case contain 3 tapes, what is the probability that one tape has 4 defects and the two remaining tape have 3 defects each?

BY WILLIAM AYINE ADONGO

ayinewilliam@yahoo.com

Actuarial Science Student– UDS