Fourier analysis of unequally spaced data.

The weighted distributions are widely used in many fields such as medicine, ecology and reliability, to name a few, for the development of proper statistical models. Weighted distributions are milestone for efficient modeling of statistical data and prediction when the standard distributions are not appropriate. A good deal of studies related to the weight distributions have been published in the literature. In this article, a brief review of these distributions is carried out. Implications of the differing weight models for future research as well as some possible strategies are discussed. Finally, characterizations of these distributions based on a simple relationship between two truncated moments are presented.

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Weighted Distributions: A Brief Review, Perspective and Characterizations

SYNOPTIC ABSTRACTA generalized version of the three-parameter transmuted inverse Weibull distribution is introduced in this article. This distribution generalizes the following distributions: (a) transmuted inverse exponential, (b) transmuted inverse Rayleigh, (c) inverse Weibull. The properties of the transmuted inverse Weibull distribution are discussed. This model is capable of modeling various shapes of aging and failure criteria. Here we present the relationship between shape parameter, probability density function, cumulative distribution function, reliability function, hazard function, percentile life, mean, variance, coefficient of variation, coefficient of skewness, and coefficient of kurtosis. We derive the moments, geometric mean, harmonic mean, entropy, mean deviation, and examine the order statistics with their moments. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. The usefulness of the new distribution is shown by ...

A New Class of Transmuted Inverse Weibull Distribution for Reliability Analysis

What we talk about when we talk about seasonality – A transdisciplinary review

This paper describes and compares several prominent single and multiple changepoint techniques for time series data. Due to their importance in inferential matters, changepoint research on correlated data has accelerated recently. Unfortunately, small perturbations in model assumptions can drastically alter changepoint conclusions; for example, heavy positive correlation in a time series can be misattributed to a mean shift should correlation be ignored. This paper considers both single and multiple changepoint techniques. The paper begins by examining cumulative sum (CUSUM) and likelihood ratio tests and their variants for the single changepoint problem; here, various statistics, boundary cropping scenarios, and scaling methods (e.g., scaling to an extreme value or Brownian Bridge limit) are compared. A recently developed test based on summing squared CUSUM statistics over all times is shown to have realistic Type I errors and superior detection power. The paper then turns to the multiple changepoint setting. Here, penalized likelihoods drive the discourse, with AIC, BIC, mBIC, and MDL penalties being considered. Binary and wild binary segmentation techniques are also compared. We introduce a new distance metric specifically designed to compare two multiple changepoint segmentations. Algorithmic and computational concerns are discussed and simulations are provided to support all conclusions. In the end, the multiple changepoint setting admits no clear methodological winner, performance depending on the particular scenario. Nonetheless, some practical guidance will emerge.

A Comparison of Single and Multiple Changepoint Techniques for Time Series Data

In this paper, a new class of weighted generalization of the Rayleigh distribution is constructed and studied. The statistical properties of these distributions including the behavior of hazard or failure rate and reverse hazard functions, moments, moment generating function, mean, variance, coecient of variation, coecient of skewness, coecient of kurtosis are obtained. Other important properties including entropy (Shannon, beta and generalized) which are measures of the uncertainty in these distributions are also presented.

/pdf/theoretical-properties-of-the-weighted-generalized-rayleigh-4qecw18jj7.pdf

Theoretical Properties of the Weighted Generalized Rayleigh and Related Distributions

This article comments on the new version of wild binary segmentation in Fryzlewicz (Ann Stat 42(6):2243–2281, 2014).

Short communication: Detecting possibly frequent change-points: wild binary segmentation 2 and steepest-drop model selection

Examples of cyclic (periodic) behavior in geophysical data abound. In many cases the primary period is known, such as in daily measurements of rain, temperature, and sea level. However, many time series of measurements contain cycles of unknown or varying length. We consider the problem of estimating the unknown period in a time series.We review the basic methods, compare their performance through a simulation studyusing observed sea level data, apply them to an astronomical data set, and discuss generalizations of the methods.

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2018EA000451

Estimating Unknown Cycles in Geophysical Data

This article studies estimation of a stationary autocovariance structure in the presence of an unknown number of mean shifts. Here, a Yule-Walker moment estimator for the autoregressive parameters in a dependent time series contaminated by mean shift changepoints is proposed and studied. The estimator is based on first order differences of the series and is proven consistent and asymptotically normal when the number of changepoints $m$ and the series length $N$ satisfies $m/N \rightarrow 0$ as $N \rightarrow \infty$

Xueheng Shi

Papers

A Comparison of Single and Multiple Changepoint Techniques for Time Series Data

Theoretical Properties of the Weighted Generalized Rayleigh and Related Distributions

Short communication: Detecting possibly frequent change-points: wild binary segmentation 2 and steepest-drop model selection

Estimating Unknown Cycles in Geophysical Data

Autocovariance Estimation in the Presence of Changepoints