PARAMETRIC MODEL Meaning and
Definition
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A parametric model refers to a statistical model that is characterized by a specific set of parameters. These parameters are numerical values that allow the model to represent and summarize data in a concise and meaningful way. In other words, a parametric model provides a mathematical function that describes the relationship between the variables involved in the model.
Parametric models are developed based on assumptions about the underlying data distribution, which makes them distinct from nonparametric models. These assumptions typically include stating the functional form of the relationship between the variables, such as linear, logistic, or exponential, as well as assumptions about the distribution of the random components of the model, such as normal or Poisson.
With parametric models, the main objective is to estimate the values of the parameters that best fit the observed data. Once the parameters are estimated, the model can be used to make predictions or infer the values of unseen data points. Parametric models are often used in various fields, including economics, finance, biology, epidemiology, and social sciences, where understanding and predicting the relationships between variables is crucial.
However, it is important to note that the usefulness of parametric models heavily relies on the correctness of the underlying assumptions. If the assumptions are inappropriate or violated, the model may not accurately represent the data, leading to biased or erroneous results.
Etymology of PARAMETRIC MODEL
The term "parametric model" is derived from the combination of two root words: "parameter" and "model".
The word "parameter" comes from the Late Latin term "parametros", meaning "limits" or "boundaries". In mathematics and statistics, a parameter refers to a numerical value that represents a characteristic of a population or a system, which remains fixed within a specific model or analysis.
The word "model" originates from the Latin term "modulus", meaning "measure" or "standard". In the context of mathematics and statistics, a model is a simplified representation or abstraction of a real-world entity or process.
Hence, when the words "parameter" and "model" are combined to form "parametric model", it refers to a statistical or mathematical model wherein the characteristics and properties of the model are defined and determined by a set of parameters.
