In oral health settings, continuous probability distributions are often used by researchers and practitioners to measure variables such as the occurrence of dental caries in a particular population, level of hypoglycemia in patients with insulin-dependent diabetes mellitus, and optimal orthodontic bonding system in the treatment of teeth irregularities (Kim & Dailey, 2008). This paper aims to increase the understanding of continuous probability distributions as used in biostatistics and public health.
In statistics, continuous probability distributions can be technically defined as a set of distributions (e.g., continuous distributions, uniform continuous distributions, normal distributions, normal approximations, exponential distributions, etc) that are used to define or describe probabilities of variables that may assume any value between two particular values, otherwise known as continuous variables (Doane & Seward, 2015). The available literature is clear that “of all the continuous probability distributions, the normal distribution is the most widely used in statistics” (Kim & Dailey, 2008, p. 94). Unlike discrete probability distributions which can be expressed using a tabular format, continuous probability distributions are described using equations or formulas as the likelihood that a continuous random variable will assume an explicit value or significance is usually zero (Doane & Seward, 2015).
The equation that is normally used by statisticians to depict a continuous probability distribution is known as the probability density function (PDF), and proceeds as follows: “the random variable Y is a function of X as demonstrated by the equation y = f(x)”; “the value of y is greater than or equal to zero for all values of x”; and “the total area under a curve of the function is equal to one” (Kim & Dailey, 2008, pp. 94-95). From these set of equations, it can be deduced that (1) the PDF is an equation that illuminates the height of the curve f(x) at each possible value of x in the assessment of a continuous random variable, (2) it is not possible for PDFs used to depict continuous probability distribution to provide negative outcomes, and (3) the area under the entire PDF must be 1 (Doane & Seward, 2015).
In general terms, continuous probability distributions can be described as encompassing a multiplicity of likely or possible distributions that may be used to describe or examine random continuous variables such as age and weight. For example, suppose that a research study aims to investigate the incidence of dental caries in children aged between five and 12 years. The age of a child recruited into the study is an example of a continuous variable since it could take any value between five and 12 years. Using the age as the continuous variable, researchers could then use one of the typologies of continuous probability distributions (e.g., uniform distribution) to know the sample age distribution between five and 12 years instead of making assumptions about the distribution in between (Kim & Dailey, 2008).
Overall, it is important to underscore the fact that the main function of continuous probability distributions is to represent the probability of continuous variables such as height, body weight, blood pressure, temperature, humidity, distance, speed, and many others. These continuous random variables can be statistically described through the use of techniques such as the cumulative distribution function and the probability density function; however, they cannot be presented as discrete variables due to their ability to be measured on a continuous scale. Lastly, it is important to note that normal distributions are the most widely used form of continuous probability distributions in most quantitative research settings due to their unimodal and symmetric characteristics.
References
Doane, D., & Seward, L. (2015). Applied statistics in business and economics (5th ed.). New York, NY: McGraw-Hill Education.
Kim, J.S., & Dailey, R.J. (2008). Biostatistics for oral healthcare. Ames, Iowa: Wiley-Blackwell.