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Elements of continuum mechanics
Published in Benjamin Loret, Fernando M. F. Simões, Biomechanical Aspects of Soft Tissues, 2017
Benjamin Loret, Fernando M. F. Simões
Actually, we know more: for positive real numbers, the arithmetic mean is larger than the geometric mean, which itself is larger than the harmonic mean, () 1n(a1+a2…an)≥a1a2…ann≥n1a1+1a2…+1an⋅
Trendsetting with some Simple Moving Measures
Published in Alan R. Jones, Best Fit Lines and Curves, and Some Mathe-Magical Transformations, 2018
If we recall from Volume II Chapter 2 (unless that was when you decided it was time to put the kettle on and missed that discussion), a Harmonic Mean is one we should consider using when we are dealing with data that is fundamentally reciprocal in nature i.e. where the ‘active’ component being used to derive a statistic is in the denominator (bottom line of a fraction or ratio.) Performance is one such statistic, measuring Target Value divided by Actual Value; the Actual Value is the ‘active’ component.
Measures of Central Tendency: Means, Modes, Medians
Published in Alan R. Jones, Probability, Statistics and Other Frightening Stuff, 2018
The principal uses of the six Measures of Central Tendency are: Arithmetic Mean: When we want a value that is representative of all possible values, and will be 'right on average'. However, this can be unduly influenced by atypical or extreme values.Mode: When we want the value that is most likely to occur above all others.Median: When we want that 'middle of the road position' with an equal chance of being under or over.Geometric Mean: When either we want to calculate the average rate that gives the same cumulative value as the product of a series of discrete rates, or we want to take the weighted position of a number of factors that are closely related but not identical for the purposes of estimating by analogy. Note: all the rates and factors must be positive — no zeros or negative values are allowed.Harmonic Mean: When we want to take the average of a set of rates where the numerator is constant, but the denominator is different. Note: all the rates must be positive — no zeros or negative values are allowed.Quadratic Mean: When we want to minimise the error or residual value when modelling a curve or straight line to some actual data using the principle of 'Least Squares'. For all the Measures of Central Tendency, the unit of measurement is the same as the data they purport to represent, e.g. feet, metres, pounds, euros, days, weeks etc.
An empirical evaluation of text representation schemes to filter the social media stream
Published in Journal of Experimental & Theoretical Artificial Intelligence, 2022
Sandip Modha, Prasenjit Majumder, Thomas Mandl
Precision, recall, and F1-score are the standard metrics that are used to evaluate classifier performance. Precision is the ratio of the number of correctly predicted positive posts to the number of total predicted positive posts. Analogously, Recall is the ratio of correctly predicted positive posts to all posts in the same class of posts. Precision considers the false positive while Recall considers the false negative. F1-score is the trade-off metric between precision and Recall. F1-score is the harmonic mean of precision and Recall. The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals.
A Secured Healthcare Management and Service Retrieval for Society Over Apache Spark Hadoop Environment
Published in IETE Journal of Research, 2023
It is a measure of harmonic mean performance that takes into account both precision and recall. The harmonic mean of two numbers tends to be closer to the smaller of the two. Both precision and recall are required to be high for harmonic mean to be high.