What Monotonic is
Monotonic is a term used to describe a function or relationship that is either increasing or decreasing over some interval. In other words, either all the values of the function are increasing or all the values are decreasing.
Steps for Monotonic:
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Determine the interval of interest: This involves deciding the range of values over which the monotonic relationship is to be tested.
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Plot the data points: Plot the data points corresponding to the interval of interest on a graph.
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Check for monotonicity: Inspect the graph and determine whether the function is either increasing or decreasing over the entire interval.
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Determine if the data is monotonic: If the data points are found to be increasing or decreasing over the entire interval, then the data is said to be monotonic.
Examples
- A monotonic relationship exists between the number of visits to a doctor and the amount of healthcare expenditure.
- A monotonic function can be used to calculate the probability of an event occurring, given a certain set of conditions.
- Monotonic regression can be used to predict future values of a variable based on historical data.
- A monotonic transformation can be used to normalize data by transforming it onto a scale that better corresponds to the underlying distribution.
- Monotonic smoothing methods can be used to remove noise from a dataset by applying a series of mathematical operations.