The frequency distribution of words has been a key object of study in statistical linguistics for the past 70 years. This distribution approximately follows a simple mathematical form known as Zipf’s law. This article first shows that human language has a highly complex, reliable structure in the frequency distribution over and above this classic law, although prior data visualization methods have obscured this fact. A number of empirical phenomena related to word frequencies are then reviewed. These facts are chosen to be informative about the mechanisms giving rise to Zipf’s law and are then used to evaluate many of the theoretical explanations of Zipf’s law in language. No prior account straightforwardly explains all the basic facts or is supported with independent evaluation of its underlying assumptions. To make progress at understanding why language obeys Zipf’s law, studies must seek evidence beyond the law itself, testing assumptions and evaluating novel predictions with new, independent data.

Zipf's word frequency law in natural language: a critical review and future directions.

The use of control charts is considered for situations in which the quality of a process or product is better characterized by a relationship between a response variable and one or more explanatory variables than by use of a univariate quality character..

Using Control Charts to Monitor Process and Product Quality Profiles

Statistical process control (SPC) methods are widely used to monitor and improve manufacturing processes and service operations. Disputes over the theory and application of these methods are frequent and often very intense. Some of the controversies and issues discussed are the relationship between hypothesis testing and control charting,the role of theory and the modeling of control chart performance,the relative merits of competing methods,the relevance of research on SPC and even the relevance of SPC itself. One purpose of the paper is to offer a resolution of some of these disagreements in order to improve the communication between practitioners and researchers.

/pdf/controversies-and-contradictions-in-statistical-process-1ngv50pzfd.pdf

Controversies and Contradictions in Statistical Process Control

What is universal about music, and what varies? We built a corpus of ethnographic text on musical behavior from a representative sample of the world's societies, as well as a discography of audio recordings. The ethnographic corpus reveals that music (including songs with words) appears in every society observed; that music varies along three dimensions (formality, arousal, religiosity), more within societies than across them; and that music is associated with certain behavioral contexts such as infant care, healing, dance, and love. The discography-analyzed through machine summaries, amateur and expert listener ratings, and manual transcriptions-reveals that acoustic features of songs predict their primary behavioral context; that tonality is widespread, perhaps universal; that music varies in rhythmic and melodic complexity; and that elements of melodies and rhythms found worldwide follow power laws.

/pdf/universality-and-diversity-in-human-song-3rg9yp983j.pdf

Universality and diversity in human song

There is considerable interest in the use of statistical process control (SPC) in healthcare. Although SPC is part of an overall philosophy of continual improvement, the implementation of SPC usually requires the production of control charts. However, as SPC is relatively new to healthcare practitioners and is not routinely featured in medical statistics texts/courses, there is a need to explain the issues involved in the selection and construction of control charts in practice. Following a brief overview of SPC in healthcare and preliminary issues, we use a tutorial-based approach to illustrate the selection and construction of four commonly used control charts (xmr-chart, p-chart, u-chart, c-chart) using examples from healthcare. For each control chart, the raw data, the relevant formulae and their use and interpretation of the final SPC chart are provided together with a notes section highlighting important issues for the SPC practitioner. Some more advanced topics are also mentioned with suggestions for further reading.

https://qualitysafety.bmj.com/content/qhc/17/2/137.full.pdf?17%2F2%2F137=

Plotting basic control charts: tutorial notes for healthcare practitioners

A synthetic control chart designed to detect shifts in the process mean can be represented as a runs rule chart with a head start feature. A Markov chain model of the synthetic control chart is proposed for the evaluation of the zero-state and steady-st..

Evaluating and Improving the Synthetic Control Chart

Zipf's Law, Music Classification, and Aesthetics

Approximate average run lengths of Shewhart charts using various trend rules are presented. It is shown that the trend rule is not effective in detecting a linear shift in the mean of the monitored process...

Performance of the Control Chart Trend Rule under Linear Shift

A study on a 220-piece corpus (baroque, classical, romantic, 12-tone, jazz, rock, DNA strings, and random music) reveals that aesthetically pleasing music may be describable under the Zipf-Mandelbrot law. Various Zipf-based metrics have been developed and evaluated. Some focus on music-theoretic attributes such as pitch, pitch and duration, melodic intervals, and harmonic intervals. Others focus on higher-order attributes and fractal aspects of musical balance. Zipf distributions across certain dimensions appear to be a necessary, but not sufficient condition for pleasant music. Statistical analyses suggest that combinations of Zipf-based metrics might be used to identify genre and/or composer. This is supported by a preliminary experiment with a neural network classifier. We describe an evolutionary music framework under development, which utilizes Zipf-based metrics as fitness functions.

Evolutionary music and the zipf-mandelbrot law: developing fitness functions for pleasant music

Average run lengths of the zone control chart are presented, The performance of this chart is compared with that of several Shewhart charts with and without runs rules, It is shown that the standard zone control chart has performance similar to some even simpler charts and a much higher false alarm rate than the Shewhart chart with all of the common runs rules. It is also shown that a slightly modified zone control chart outperforms the Shewhart chart with the common runs rules.

Robert B. Davis

Papers

Evaluating and Improving the Synthetic Control Chart

Zipf's Law, Music Classification, and Aesthetics

Performance of the Control Chart Trend Rule under Linear Shift

Evolutionary music and the zipf-mandelbrot law: developing fitness functions for pleasant music

Performance of the zone control chart