Probability-Distributions-and-Data-Modeling.pdf

1. Probability
Distributions and Data
Modeling

2. Bernoulli Distribution
- characterizes a random variable
having two possible outcomes, each
with a constant probability of
occurrence
- success (x = 1) having probability p
- failure (x = 0) having probability 1-p

3. Bernoulli Distribution
Ex.
coin tossing
Application in Business
*might be used to model whether an
individual responds positively (x=1) or negatively
(x=0) to a telemarketing promotion
marble experiment

4. Binomial Distribution
- models n independent replications of
a Bernoulli experiment, each with a
probability p of success
- the random variable X represents the
number of successes in these n
experiments

5. Binomial Distribution
Ex.
covid-19 positive or negative
medicine trial
Rental Shop

6. Poisson Distribution
- discrete distribution used to model the
number of occurrences in some unit of
measure
- assumes no limit on the number of
occurrences, that occurrences are
independent, and that the average
number of occurrences per unit Is constant

7. Poisson Distribution
Ex.
biology – mutation detection
disaster readiness
staffing and scheduling

8. Uniform Distribution
- continuous probability distribution
and is concerned wit events that are
equally likely to occur
- each value in the set of possible
values has the same exact possibility of
happening

9. Uniform Distribution
Ex.
Deck of Cards
Inventory Management

10. Normal Distribution
- continuous distribution that is
described by the familiar bell-shaped
curve
- most important distribution used in
statistics
- mean and standard deviation

11. Normal Distribution
Ex.
human height and weight
test scores
Nokia

12. Exponential Distribution
- continuous distribution that models
the time between randomly occurring
events
- refers to the amount of time until
some specific event occurs

13. Exponential Distribution
Ex.
time between failures of machine
amount of time until an earthquake
occurs
time between customer arrivals to a
service system

14. Data Modeling and Distribution
Fitting
In many applications of business
analytics, data of important variables
such as customer demand, purchase
behavior, machine failure times and
service activity times need to be
collected to gain understanding of
distributions.

15. Data Modeling and Distribution
Fitting
 Probability distribution fitting or simply distribution fitting is
the fitting of a probability distribution to a series of data
concerning the repeated measurement of a variable
phenomenon.
 The aim of distribution fitting is
to predict the probability or to forecast the frequency of
occurrence of the magnitude of the phenomenon in a
certain interval.


16. Goodness of Fit
- statistical procedure that is basis for
fitting data to a probability distribution
- attempts to draw a conclusion about
the nature of the distribution

17. Distribution Fitting with Analytic
Solver Platform
Analytic Solver Platform
- has the capability of “fitting” a
probability distribution to data using one
of the three goodness-of-fit procedures

18. Thank you
and
God bless