 # Discrete Distribution

## Definition

A Discrete Distribution in finance refers to a statistical distribution that represents variables that take distinct or separate values. These variables can be counted as distinct events, such as the number of times a particular outcome occurs. Examples include binomial or Poisson distributions.

### Phonetic

The phonetic spelling of “Discrete Distribution” would be:Discrete: /dɪˈskriːt/Distribution: /ˌdɪstrɪˈbjuːʃən/

## Key Takeaways

1. Definition: A discrete distribution refers to a statistical distribution that shows the probabilities of outcomes of a discrete random variable. A discrete random variable is a variable that can only take on a certain number of values – these values can be finite or countably infinite.
2. Examples: Examples of discrete distributions include the Poisson distribution, which models the number of times an event occurs in a fixed interval of time or space, and the Binomial distribution, which models the number of successes in a fixed number of Bernoulli trials.
3. Usage: Discrete distributions are particularly useful in real-world applications such as predicting customer arrivals at a store, quality control in manufacturing, or in medical or environmental research outcomes where the outcome variables are limited to discrete values.

## Importance

Discrete Distribution is important in business and finance for various reasons. It is a statistical term used to represent the probability of occurrence of distinct outcomes. It plays a significant role in risk management and decision making. With this distribution, financial analysts can predict future patterns, investment returns or stock price movements by analyzing past data and identifying the probability of specific outcomes. Hence, this tool aids organizations in making informed decisions, undertaking risk assessments, enhancing the effectiveness of strategies, and ultimately, boosting their financial performance.

## Explanation

The primary purpose of a discrete distribution in finance/business is to quantify the probability of occurrence of distinct or separate events. It provides a mathematical framework for dealing with scenarios where outcomes are precisely defined. This statistical model helps to gauge uncertainties and manage expectations in financial forecasting, risk management, and strategic decision-making process. It is especially useful where the variables of interest are integers and the possibilities are countable, such as the number of cars sold in a month or the number of defaulted loans in a portfolio.A prime application of discrete distribution is portfolio risk analysis. For instance, a financial analyst can use a discrete probability distribution to quantify the likelihood of different potential returns of an investment portfolio, assisting investors in risk assessment and selection of investment strategies. It also plays a crucial role in option pricing models, where discrete distribution enables option traders to price binary options. Overall, whether it’s for analyzing sales data, projecting profit margins, determining insurance premiums, quantifying credit risk or modeling stock prices, the usage of discrete distribution is vast and varied in business and finance.

## Examples

1. Tossing A Coin: Every coin toss has a discrete distribution. There are only two possible outcomes – heads or tails. The probability of getting either heads or tails is 0.5, showing a classic example of a discrete distribution. The outcome cannot be a fraction, it must be a whole value, and each outcome is independent of the previous ones.2. Sales of a Particular Product: Suppose a company tracks the sales of a particular product which can be sold in whole units only (like cars, or laptops). They can predict the discrete number of units they expect to sell every quarter, with each number of units (0, 1, 2, …) having a corresponding probability. The probabilities create a discrete distribution.3. Number of Phone Calls at a Call Center: Another real-world example of discrete distribution may be in a customer service department of a company. They can analyze the number of phone calls they receive within a given period. The number could be 0, 1, 2, 3, or even 100, but never a fraction. And the probability of getting each call is associated with each discrete point, creating a discrete distribution.

What is a Discrete Distribution?

A discrete distribution is a statistical term referring to a type of probability distribution that can take on a finite or countably infinite number of values. This can refer to outcomes of experiments or situations such as rolling a die, where the possible results are discrete, rather than continuous.

What is an example of a Discrete Distribution?

An example of discrete distribution is the Bernoulli distribution. In the Bernoulli distribution, there are only two possible results, often labelled as success and failure. Another common example is the Poisson distribution, which models the number of times an event occurs within a specific time or space.

How are Discrete Distributions used in Finance and Business?

Discrete distributions are commonly used in finance and business to model scenarios with outcomes that are countable. For example, companies may use them to predict the number of products they’ll sell in a day, or the number of calls received in a call center per hour.

What are the main differences between Discrete Distributions and Continuous Distributions?

The main difference between discrete and continuous distributions lies in the types of variables they represent. Discrete distributions represent variables that are countable and have distinct separation between them whereas continuous distributions pertain to variables with a potentially infinite and uncountable set of values.

How can we interpret or read a Discrete Distribution?

In a discrete distribution, the probability of an outcome is represented by the height of the bar over that outcome value on the graph. The sum of all outcome probabilities always equals one.

Can you mention any statistical tests that use Discrete Distribution?

Yes, the chi-square test for goodness of fit, the binomial test, and the Poisson distribution model are all examples of statistical tests that use discrete distributions.

What are the potential challenges or limitations in working with Discrete Distributions?

One limitation of discrete distributions is that they cannot be used to model all types of data, especially data that is continuous in nature. Another challenge is that estimating the parameters of a discrete distribution can be statistically complex and challenging.

Can Discrete Distribution results have decimal or fraction numbers?

No, in discrete distributions, the outcomes are distinct countable values, and cannot be a fraction or a decimal. They are whole, specific numbers. For example, you cannot sell 0.5 or 2.3 products. However, probabilities of these outcomes can be fractions or decimals.