Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means. In other words, the ANOVA is used to test the difference between two or more means.
Lyra is a small constellation. It is one of the 48 listed by the 2nd century astronomer Ptolemy, and is one of the modern 88 constellations recognized by the International Astronomical Union. Lyra was often represented on star maps as a vulture or an eagle carrying a lyre, and hence is sometimes referred to as Vultur Cadens or Aquila Cadens, respectively. Beginning at the north, Lyra is bordered by Draco, Hercules, Vulpecula, and Cygnus. Lyra is nearly overhead in temperate northern latitudes shortly after midnight at the start of summer. From the equator to about the 40th parallel south it is visible low in the northern sky during the same months.
A variable star is a star whose brightness as seen from Earth changes systematically with time. This variation may be caused by a change in emitted light or by something partly blocking the light, so variable stars are classified as either:
In astronomy, a light curve is a graph of the light intensity of a celestial object or region as a function of time, typically with the magnitude of light received on the y-axis and with time on the x-axis. The light is usually in a particular frequency interval or band.
RR Lyrae variables are periodic variable stars, commonly found in globular clusters. They are used as standard candles to measure (extra) galactic distances, assisting with the cosmic distance ladder. This class is named after the prototype and brightest example, RR Lyrae.
Linear trend estimation is a statistical technique used to analyze data patterns. Data patterns, or trends, occur when the information gathered tends to increase or decrease over time or is influenced by changes in an external factor. Linear trend estimation essentially creates a straight line on a graph of data that models the general direction that the data is heading.
Test statistic is a quantity derived from the sample for statistical hypothesis testing. A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test. In general, a test statistic is selected or defined in such a way as to quantify, within observed data, behaviours that would distinguish the null from the alternative hypothesis, where such an alternative is prescribed, or that would characterize the null hypothesis if there is no explicitly stated alternative hypothesis.
The Fast-Folding Algorithm (FFA) is a computational method primarily utilized in the domain of astronomy for detecting periodic signals. FFA is designed to reveal repeating or cyclical patterns by "folding" data, which involves dividing the data set into numerous segments, aligning these segments to a common phase, and summing them together to enhance the signal of periodic events. This algorithm is particularly advantageous when dealing with non-uniformly sampled data or signals with a drifting period, which refer to signals that exhibit a frequency or period drifting over space and time, such cycles are not stable and consistent; rather, they are randomized. A quintessential application of FFA is in the detection and analysis of pulsars—highly magnetized, rotating neutron stars that emit beams of electromagnetic radiation. By employing FFA, astronomers can effectively distinguish noisy data to identify the regular pulses of radiation emitted by these celestial bodies. Moreover, the Fast-Folding Algorithm is instrumental in detecting long-period signals, which is often a challenge for other algorithms like the FFT that operate under the assumption of a constant frequency. Through the process of folding and summing data segments, FFA provides a robust mechanism for unveiling periodicities despite noisy observational data, thereby playing a pivotal role in advancing our understanding of pulsar properties and behaviors.
Least-squares spectral analysis (LSSA) is a method of estimating a frequency spectrum based on a least-squares fit of sinusoids to data samples, similar to Fourier analysis. Fourier analysis, the most used spectral method in science, generally boosts long-periodic noise in the long and gapped records; LSSA mitigates such problems. Unlike in Fourier analysis, data need not be equally spaced to use LSSA.
S Arae (S Ara) is an RR Lyrae-type pulsating variable star in the constellation of Ara. It has an apparent visual magnitude which varies between 9.92 and 11.24 during its 10.85-hour pulsation period, and it exhibits the Blazhko effect.
In probability theory and statistics, the index of dispersion, dispersion index, coefficient of dispersion, relative variance, or variance-to-mean ratio (VMR), like the coefficient of variation, is a normalized measure of the dispersion of a probability distribution: it is a measure used to quantify whether a set of observed occurrences are clustered or dispersed compared to a standard statistical model.
SigSpec is a statistical technique to provide the reliability of periodicities in a measured time series. It relies on the amplitude spectrum obtained by the Discrete Fourier transform (DFT) and assigns a quantity called the spectral significance to each amplitude. This quantity is a logarithmic measure of the probability that the given amplitude level would be seen in white noise, in the sense of a type I error. It represents the answer to the question, “What would be the chance to obtain an amplitude like the measured one or higher, if the analysed time series were random?”
Stellar pulsations are caused by expansions and contractions in the outer layers as a star seeks to maintain equilibrium. These fluctuations in stellar radius cause corresponding changes in the luminosity of the star. Astronomers are able to deduce this mechanism by measuring the spectrum and observing the Doppler effect. Many intrinsic variable stars that pulsate with large amplitudes, such as the classical Cepheids, RR Lyrae stars and large-amplitude Delta Scuti stars show regular light curves.
Seismic inversion involves the set of methods which seismologists use to infer properties through physical measurements. Surface-wave inversion is the method by which elastic properties, density, and thickness of layers in the subsurface are obtained through analysis of surface-wave dispersion. The entire inversion process requires the gathering of seismic data, the creation of dispersion curves, and finally the inference of subsurface properties.
V473 Lyrae is a variable star in the constellation Lyra. It is an unusual Classical Cepheid variable with a visual range of 5.99 to 6.35.
HN Pegasi is the variable star designation for a young, Sun-like star in the northern constellation of Pegasus. It has an apparent visual magnitude of 5.9, which, according to the Bortle scale, indicates that it is visible to the naked eye from suburban skies. Parallax measurements put the star at a distance of around 59 light years from the Sun, but it is drifting closer with a radial velocity of −16.7 km/s.
DY Pegasi, abbreviated DY Peg, is a binary star system in the northern constellation of Pegasus. It is a well-studied SX Phoenicis variable star with a brightness that ranges from an apparent visual magnitude of 9.95 down to 10.62 with a period of 1.75 hours. This system is much too faint to be seen with the naked eye, but can be viewed with large binoculars or a telescope. Based on its high space motion and low abundances of heavier elements, it is a population II star system.
TU Ursae Majoris is a variable star in the northern circumpolar constellation of Ursa Major. It is classified as a Bailey-type 'ab' RR Lyrae variable with a period of 0.557648 days that ranges in brightness from apparent visual magnitude of 9.26 down to 10.24. The distance to this star is approximately 2,090 light years based on parallax measurements. It is located near the north galactic pole at a distance that indicates this is a member of the galactic halo.
Trend periodic non-stationary processes are a type of cyclostationary process that exhibits both periodic behavior and a statistical trend. The trend can be linear or nonlinear, and it can result from systematic changes in the data over time. A cyclostationary process can be formed by removing the trend component. This approach is utilized in the analysis of the trend-stationary process.
