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🔗 Mathematics 🔗 Statistics

The Gompertz curve or Gompertz function is a type of mathematical model for a time series, named after Benjamin Gompertz (1779–1865). It is a sigmoid function which describes growth as being slowest at the start and end of a given time period. The right-side or future value asymptote of the function is approached much more gradually by the curve than the left-side or lower valued asymptote. This is in contrast to the simple logistic function in which both asymptotes are approached by the curve symmetrically. It is a special case of the generalised logistic function. The function was originally designed to describe human mortality, but since has been modified to be applied in biology, with regard to detailing populations.

🔗 Mathematics 🔗 Statistics 🔗 Psychology

Accuracy and precision are two measures of observational error. Accuracy is how close a given set of measurements (observations or readings) are to their true value. Precision is how close the measurements are to each other.

The International Organization for Standardization (ISO) defines a related measure: trueness, "the closeness of agreement between the arithmetic mean of a large number of test results and the true or accepted reference value."

While precision is a description of random errors (a measure of statistical variability), accuracy has two different definitions:

1. More commonly, a description of systematic errors (a measure of statistical bias of a given measure of central tendency, such as the mean). In this definition of "accuracy", the concept is independent of "precision", so a particular set of data can be said to be accurate, precise, both, or neither. This concept corresponds to ISO's trueness.
2. A combination of both precision and trueness, accounting for the two types of observational error (random and systematic), so that high accuracy requires both high precision and high trueness. This usage corresponds to ISO's definition of accuracy (trueness and precision).

🔗 Mathematics 🔗 Statistics 🔗 Linguistics 🔗 Linguistics/Applied Linguistics

Zipf's law (, not as in German) is an empirical law formulated using mathematical statistics that refers to the fact that many types of data studied in the physical and social sciences can be approximated with a Zipfian distribution, one of a family of related discrete power law probability distributions. Zipf distribution is related to the zeta distribution, but is not identical.

Zipf's law was originally formulated in terms of quantitative linguistics, stating that given some corpus of natural language utterances, the frequency of any word is inversely proportional to its rank in the frequency table. Thus the most frequent word will occur approximately twice as often as the second most frequent word, three times as often as the third most frequent word, etc.: the rank-frequency distribution is an inverse relation. For example, in the Brown Corpus of American English text, the word the is the most frequently occurring word, and by itself accounts for nearly 7% of all word occurrences (69,971 out of slightly over 1 million). True to Zipf's Law, the second-place word of accounts for slightly over 3.5% of words (36,411 occurrences), followed by and (28,852). Only 135 vocabulary items are needed to account for half the Brown Corpus.

The law is named after the American linguist George Kingsley Zipf (1902–1950), who popularized it and sought to explain it (Zipf 1935, 1949), though he did not claim to have originated it. The French stenographer Jean-Baptiste Estoup (1868–1950) appears to have noticed the regularity before Zipf. It was also noted in 1913 by German physicist Felix Auerbach (1856–1933).