General Statistical Properties Research Articles

A new power G-family of distributions: Properties, estimation, and applications.

This article suggests a new method to expand a family of life distributions by adding a parameter to the family, increasing its flexibility. It is called the extended Modi-G family of distributions. We derived the general statistical properties of the proposed family. Different methods of estimation were presented to estimate the parameters for the proposed family, such as maximum likelihood, ordinary least square, weighted least square, Anderson Darling, right-tailed Anderson-Darling, Cramér-von Mises, and maximum product of spacing methods. A special sub-model with three parameters called extended Modi exponential distribution was derived along with different shapes of its density and hazard functions. Randomly generated data sets and different estimation methods were used to illustrate the behavior of parameters of the proposal sub-model. To illustrate the importance of the proposed family over the other well-known methods, applications to medicine and geology data sets were analyzed.

Finding the Particularity of the Active Episode of SGR J1935+2154 during Which FRB 20200428 Occurred: Implication from Statistics of Fermi/GBM X-Ray Bursts

By using the Fermi/Gamma-ray Burst Monitor data of the X-ray bursts (XRBs) of SGR J1935+2154, we investigate the temporal clustering of the bursts and the cumulative distribution of the waiting time and fluence/flux. It is found that the bursts occurring in the episode hosting FRB 20200428 have obviously shorter waiting times than those in the other episodes. The general statistical properties of the XRBs further indicate they could belong to a self-organized critical system (e.g., starquakes), making them very similar to the earthquake phenomena. Then, according to a unified scaling law between the waiting time and energy of the earthquakes as well as their aftershocks, we implement an analogy analysis on the XRBs and find that the fast radio burst (FRB) episode owns more dependent burst events than the other episodes. It is indicated that the FRB emission could be produced by the interaction between different burst events, which could correspond to a collision between different seismic/Alfvén waves or different explosion outflows. Such a situation could appear when the magnetar enters into a global intensive activity period.

Entropic property of randomized QAOA circuits

Quantum approximate optimization algorithm (QAOA) aims to solve discrete optimization problems by sampling bitstrings using a parameterized quantum circuit. The circuit parameters (angles) are optimized in the way that minimizes the cost Hamiltonian expectation value. Recently, general statistical properties of QAOA output probability distributions have begun to be studied. In contrast to the conventional approach, we analyse QAOA circuits with random angles. We provide analytical equations for probabilities and the numerical evidence that for unweighted Max-Cut problems on connected graphs such sampling always gives higher entropy of energy distribution than uniform random sampling of bitstrings. We also analyse the probability to obtain the global optima, which appears to be higher on average than for random sampling.

Different Estimation Methods for New Probability Distribution Approach Based on Environmental and Medical Data

In this article, we introduce a new extension of the power Lomax (PLo) model by combining the type II exponentiated half-logistic class of statistical models and the PLo model. The new suggested statistical model called type II exponentiated half-logistic-PLo (TIIEHL-PLo) model. However, the new TIIEHL-PLo model is more flexible and applicable than the PLo model and some extensions of THE PLo model, especially those in environmental and medical fields. Some general statistical properties of the TIIEHL-PLo model are computed. Six different estimation approaches, namely maximum likelihood (ML), least-square (LS), weighted least-squares (WLS), maximum product spacing (MPS), Cramér–von Mises (CVM), and Anderson–Darling (AD) estimation approaches, are utilized to estimate the parameters of the TIIEHL-PLo model. The simulation experiment examines the accuracy of the model parameters by employing six different methodologies of estimation. In this study, we analyze three real datasets from the environmental and medical fields to highlight the relevance and adaptability of the proposed approach. The newly suggested model is exceptionally adaptable and outperforms several well-known statistical models.

A Note on the Estimation of the Maximum Possible Earthquake Magnitude Based on Extreme Value Theory for the Groningen Gas Field

ABSTRACT Extreme value statistics is a popular and frequently used tool to model the occurrence of large earthquakes. The problem of poor statistics arising from rare events is addressed by taking advantage of the validity of general statistical properties in asymptotic regimes. In this note, I argue that the use of extreme value statistics for the purpose of practically modeling the tail of the frequency–magnitude distribution of earthquakes can produce biased and thus misleading results because it is unknown to what degree the tail of the true distribution is sampled by data. Using synthetic data allows to quantify this bias in detail. The implicit assumption that the true Mmax is close to the maximum observed magnitude Mmax,observed restricts the class of the potential models a priori to those with Mmax=Mmax,observed+ΔM with an increment ΔM≈0.5…1.2. This corresponds to the simple heuristic method suggested by Wheeler (2009) and labeled “Mmax equals Mobs plus an increment.” The incomplete consideration of the entire model family for the frequency–magnitude distribution neglects, however, the scenario of a large so far unobserved earthquake.

Thermal awareness to enhance data center energy efficiency

Data centers aim at provisioning on-demand processing, storage and networking capabilities in a reliable and scalable way. In this context, proper maintenance of IT equipment within data center (DC) premises is crucial as it ensures prolonged lifetime of servers and uninterrupted availability of resources. This paper focuses on the analysis how the exact temperatures in a real big DC cluster of 10 368 cores correspond to thermal guidelines for IT devices. Available readings of servers exhaust air temperature, inlet air temperature, as well as CPUs temperature have been analyzed to uncover general statistical properties which are subsequently aggregated into several descriptive metrics that reveal global and local trends. The ultimate outcome of this research is the improvement of DC thermal management for sustainable operations via a set of recommendations.

The Fermi–Dirac distribution provides a calibrated probabilistic output for binary classifiers

Binary classification is one of the central problems in machine-learning research and, as such, investigations of its general statistical properties are of interest. We studied the ranking statistics of items in binary classification problems and observed that there is a formal and surprising relationship between the probability of a sample belonging to one of the two classes and the Fermi-Dirac distribution determining the probability that a fermion occupies a given single-particle quantum state in a physical system of noninteracting fermions. Using this equivalence, it is possible to compute a calibrated probabilistic output for binary classifiers. We show that the area under the receiver operating characteristics curve (AUC) in a classification problem is related to the temperature of an equivalent physical system. In a similar manner, the optimal decision threshold between the two classes is associated with the chemical potential of an equivalent physical system. Using our framework, we also derive a closed-form expression to calculate the variance for the AUC of a classifier. Finally, we introduce FiDEL (Fermi-Dirac-based ensemble learning), an ensemble learning algorithm that uses the calibrated nature of the classifier's output probability to combine possibly very different classifiers.

The Flexible Burr X-G Family: Properties, Inference, and Applications in Engineering Science

In this paper, we introduce a new flexible generator of continuous distributions called the transmuted Burr X-G (TBX-G) family to extend and increase the flexibility of the Burr X generator. The general statistical properties of the TBX-G family are calculated. One special sub-model, TBX-exponential distribution, is studied in detail. We discuss eight estimation approaches to estimating the TBX-exponential parameters, and numerical simulations are conducted to compare the suggested approaches based on partial and overall ranks. Based on our study, the Anderson–Darling estimators are recommended to estimate the TBX-exponential parameters. Using two skewed real data sets from the engineering sciences, we illustrate the importance and flexibility of the TBX-exponential model compared with other existing competing distributions.

The Reflected-Shifted-Truncated Lindley Distribution with Applications

AbstractIn this paper, a new probability density function with bounded domain is presented. The new distribution arises from the Lindley distribution proposed in 1958. It presents the advantage of not including any special function in its formulation. The new transformed model, called the reflected-shifted-truncated Lindley distribution can be used to model left-skewed data. We provide a comprehensive treatment of general mathematical and statistical properties of this distribution. We estimate the model parameters by maximum likelihood methods based on complete and right-censored data. To assess the performance and consistency of the maximum likelihood estimators, we conduct a simulation study with varying sample sizes. Finally, we use the distribution to model left-skewed survival and failure data from two real data sets. For the real data sets containing complete data and right-censored data, this distribution is superior in its ability to sufficiently model the data as compared to the power Lindley, exponentiated power Lindley, generalized inverse Lindley, generalized weighted Lindley and the well-known Gompertz distributions.

The Marshall-Olkin Topp Leone-G family of distributions: A family for generalizing probability models

This paper introduced a family of distributions which is flexible and capable of yielding more robust compound probability models when used in modeling real life events. General statistical properties of the family; Marshall-Olkin Topp Leone-G family of distributions were adequately provided. For illustration purpose, the Marshall-Olkin Topp Leone Weibull distribution was applied to three real life data sets and it is undoubtedly better than its competitors; Marshall Olkin Topp Leone Burr XII, Marshall Olkin Topp Leone Lomax, Beta Weibull, Kumaraswamy Weibull (KuWe), Exponentiated Generalized Weibull (EGWe) and Weibull Weibull (WeWe) distributions. Simulation studies were also provided to investigate the behavior of the parameters.

A simple wavelet-based test for serial correlation in panel data models

Hong and Kao (2004) proposed a class of general applicable wavelet-based tests for serial correlation of unknown form in the residuals from a panel regression model. The tests can be applied to both static and dynamic panel models. Their test, however, is computationally difficult to implement, and simulation studies show that the test has poor small-sample properties. In this paper, we extend Gençay’s (2010) time-series test for serial correlation to panel data case. Our new test is also wavelet based and maintains the advantages of the Hong and Kao (2004) test, but it is much simpler and easier to implement. Furthermore, simulation results show that our test has quicker convergence rate and hence better small-sample properties, compared to Hong and Kao (2004) test. We also compare our test with several other existing tests for series correlation, and our test has in general better statistical properties in terms of both size and power.

Modified multi-dimensional q-deformed Newton oscillators: Algebra, interpolating statistics and thermodynamics

In this work, we present a new algebraic modelby constructing the modified multi-dimensional q-deformed bosonic and fermionic Newton oscillator algebras. This construction leads effectively to describe interpolating statistics, which can be used to approach the properties of quasi-particle excitations occurring in many-body interacting quantum systems. It is shown that the model algebras are endowed with the SUφ(d)- and SUθ(d)-symmetries, where φ and θ are real parameters describing the special phase shifts between two different modes of the models. Particular emphasis is given to the two-dimensional case, which reveals a suitable framework for analyzing anyonic behavior of the models. Furthermore, we discuss the effects of deformation on the general thermodynamical and statistical properties of gas models of these interpolating statistics particles such as the q-deformed statistical distribution function and the equation of state in two and three dimensions. Finally, we concisely point out other possible physical applications of the present deformed (quasi)particle models.

Void galaxies in the nearby Universe – I. Sample description

The main goal of this work is to form a large, deep and representative sample of dwarf galaxies residing in voids of the nearby Universe. The formed sample is the basement for the comprehensive mass study of the galaxy content, their evolutionary status, clustering and dynamics with respect to their counterparts residing in more typical, denser regions and for study of void small-scale substructures. We present 25 voids over the entire sky within 25 Mpc from the Local Group. They are defined as groups of lumped empty spheres bounded by `luminous' galaxies with the absolute K-band magnitudes brighter than -22.0. The identified void regions include the Local Void and other known nearby voids. The nearest nine voids occupy a substantial part of the Local Volume. Of the total number of 6792 cataloged galaxies in the considered volume, 1354 objects fall into 25 nearby voids. Of this general void galaxy sample, we separate the sub-sample of `inner' void galaxies, residing deeper in voids, with distances to the nearest luminous galaxy DNN > 2.0 Mpc. The `inner' galaxy sample includes 1088 objects, mostly dwarfs with MB distribution peaked near -15.0 and extending down to -7.5 mag. Of them, 195 fall in the Local Volume (space within R=11 Mpc). We present the general statistical properties of this Nearby Void Galaxy sample and discuss the issues related to the sample content and the prospects of its use.

Hybrid modeling of quasi-particles: Algebra, Fock space and condensation

In this study, we first introduce a new quasi-particle algebra, which enables us to effectively describe a unified framework for both bosons and fermions. We then study general thermodynamical and statistical properties of a hybrid-type gas model of these quasi-particles. In this context, we specifically focus on the conditions under which the hybrid-type quasi-particle gas condensation would occur in the present model. The results obtained in this work reveal that the present gas model of quasi-particles can be used to approximate non-linear behavior observed in composite particle systems such as in studies on the phenomenon of high-Tc superconductivity in a given material.

Modeling Discrete Bivariate Data with Applications to Failure and Count Data

In this study, we propose a new class of flexible bivariate distributions for discrete random variables. The proposed class of distribution is based on the notion of conditional failure rate for a discrete‐type random variable. We derive general formulae for the joint distributions belonging to the proposed class that, unlike other discrete bivariate models already proposed in the literature such as the well‐known and most popular Holgate's bivariate Poisson distribution, can model both positive and negative dependence. We discuss general statistical properties of the proposed class as well. Specific families of bivariate distributions can be generated from the general class proposed in this paper just by specifying the ‘baseline distributions’. Furthermore, specific discrete bivariate distributions belonging to the proposed class are applied to analyze three real data sets, and the results are compared with those obtained from conventional models. Copyright © 2017 John Wiley & Sons, Ltd.

Mathematical Analysis of a Coarsening Model with Local Interactions

We consider particles on a one-dimensional lattice whose evolution is governed by nearest-neighbor interactions where particles that have reached size zero are removed from the system. Concentrating on configurations with infinitely many particles, we prove existence of solutions under a reasonable density assumption on the initial data and show that the vanishing of particles and the localized interactions can lead to non-uniqueness. Moreover, we provide a rigorous upper coarsening estimate and discuss the generic statistical properties as well as some non-generic behavior of the evolution by means of heuristic arguments and numerical observations.

General and specific statistical properties of foreign exchange markets during a financial crash

We investigate minute-by-minute foreign exchange rate (FX) data of 14 currencies with different exchange-rate regimes during a financial crash, and divide these data into several stages according to their respective tendencies: depreciation stage (stage 1), fluctuating stage (stage 2), and appreciation stage (stage 3). The tail distribution of FX rate returns satisfies a power-law structure for different types of currencies. We find the absolute value of the power-law exponent is smaller in emerging markets than in developed markets, especially during the stage 1, and is greatest in pegged currencies.We also find that the correlation properties of the FX rate return series have quite disparate results among the various types of currencies. Currencies in developed markets respectively have weak persistence and anti-persistence in short and long timescales; whereas the pegged currencies and currencies in emerging markets show different degrees of anti-persistence in various timescales. Further analyses on the data in divided stages indicate that emerging markets and pegged currencies have more prominent dual fractal structures after the depreciation stage, while the developed markets do not. Hurst exponent analyses on the sign series yield similar results to that on the original return series for most currencies. The magnitude series of the returns provide some unique results during a crash. The developed market currencies have strong persistence and exhibit a weaker correlation in the depreciation and appreciation stages. In contrast, the currencies of emerging markets as well as pegged currencies fail to show such a transformation, but rather show a constant-correlation behavior in the corresponding stages of a crash. These results indicate that external shocks exert different degrees of influence during different stages of the crash in various markets.

Skew-Type I Generalized Logistic Distribution and its Properties

Generalized logistic distributions are very versatile and give useful representations of many physical situations. Skew-symmetric densities recently received much attention in the literature. In this paper, we introduce a new class of skew-symmetric distributions which are formulated based on cumulative distributions of skew-symmetric densities. We derive, the probability density function (pdf) and cumulative distribution function (CDF) of the skew type I generalized logistic distribution denoted by S'GLD . The general statistical properties of the S'GLD such as: the moment generating function (mgf), characteristic function (chf), Laplace and Fourier transformations are obtained in explicit form. Expressions for the n th moment, skewness and kurtosis are discussed. Mean deviation about the mean and about the median, Renye entropy and the order statistics are also given. We consider the general case by inclusion of location and scale parameters. The results of Nadarajah (2009) are obtained as special cases. Graphical illustration of some results has been represented. Further we present a numerical example to illustrate some results of this paper.

What is Known About Hedge Funds?

In this article, we provide the busy reader with a survey of articles that were written over the past four years on hedge funds. Specifically, we review the economic basis for hedge fund returns and then discuss some of the logical consequences of these observations. Next, we summarize the general statistical properties of hedge fund strategies. We then examine what the appropriate performance measurement and risk management techniques are for these investments. And lastly, we briefly cover ways that investors can consider incorporating hedge funds within their overall portfolios.

Consistency of maximum likelihood estimation for some dynamical systems

We consider the asymptotic consistency of maximum likelihood parameter estimation for dynamical systems observed with noise. Under suitable conditions on the dynamical systems and the observations, we show that maximum likelihood parameter estimation is consistent. Our proof involves ideas from both information theory and dynamical systems. Furthermore, we show how some well-studied properties of dynamical systems imply the general statistical properties related to maximum likelihood estimation. Finally, we exhibit classical families of dynamical systems for which maximum likelihood estimation is consistent. Examples include shifts of finite type with Gibbs measures and Axiom A attractors with SRB measures.