Basic Statistical Properties Research Articles

Generalized Poisson integer-valued autoregressive processes with structural changes

In this paper, we introduce a new first-order generalized Poisson integer-valued autoregressive process, for modeling integer-valued time series exhibiting a piecewise structure and overdispersion. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares and conditional maximum likelihood estimators are derived. The asymptotic properties of the estimators are established. Moreover, two special cases of the process are discussed. Finally, some numerical results of the estimates and a real data example are presented.

The Theoretical Overview of Generalized Gumbel Type-Ⅱ Distribution

A new version of weighted model is introduced by assigning weights to Gumbel Distribution Type Ⅱ (GDT-Ⅱ) to make it more useful and flexible in life time data .This paper provides an understanding of some basic statistical properties of (WGDT-Ⅱ).It includes moments and maximum likelihood estimator. In addition to the above it imparts the insight to distribution function, survival rate, hazard rate and reverse hazard rate. The behavior of PDF, CDF, and Survival rate, Hazard rates and Reverse Hazard rates has been presented through various graphs by setting different values of parameters.

Extended Bernstein-Kantorovich-Stancu Operators with Multiple Parameters and Approximation Properties

In this paper, we introduce a novel extension of the Bernstein-Kantorovich-Stancu type operator of degree n with the help of multiple shape parameters. Voronovskaja and Grüss-Voronovskaja type approximation theorems are examined via Ditzian-Totik moduli of smoothness. We investigate basic statistical convergence properties with respect to a non-negative regular summability matrix. Moreover, using Ditzian-Totik moduli, local and global approximation properties associated to the proposed operator have been established. Finally, several illustrative examples are presented to demonstrate the efficiency, applicability and validity of the operator. The graphical and numerical results verify that the proposed operator gives better approximation as well as expand the previous Bernstein-Kantorovich type modifications including single parameter.

THE COINTEGRATION RELATIONSHIP BETWEEN BITCOIN AND THE STOCK INDICES OF TURKEY AND BRICS COUNTRIES

Bitcoin, the most important of all cryptocurrencies, is a currency that is not included in the central monetary system and has a digital format. With the rapid increase in the value of Bitcoin in recent years, it has attracted the attention of investors. Bitcoin, as an alternative to traditional investment tools, has sparked a lot of controversies. In this study, the Bitcoin price relationship between stock market indices and the BRICS countries belonging to Turkey is intended to be detected. In this direction of Bitcoin 01.01.2013-31.12.2019 period to test the relationship between Turkey and the BRICS countries, stock index monthly data are used. After determining the basic statistical properties of the series, cointegration and causality test was performed to determine the financial relationship. ADF (Augmented Dickey-Fuller) unit root tests and stationarity analysis are applied, and then the existence of long-term relationships between stock exchanges is explained with the Johansen cointegration test. The Vector Error Correction Model (VECM) was used to analyze whether the long-term relationship is in equilibrium. Also, short-term relationships were determined by Granger causality analysis. The analysis performed between variables were identified as a result of a long-term relationship, Russia (MOEX) and Turkey (BIST100) was found to be the cause of the stock market index of Bitcoin. It has been determined that Bitcoin is the cause of China (SHANGAI) exchange. In these exchanges, it has been observed that the change in Bitcoin prices in the short term affects investment decisions.

On the unit Burr-XII distribution with the quantile regression modeling and applications

In this paper, we modify the Burr-XII distribution through the inverse exponential scheme to obtain a new two-parameter distribution on the unit interval called the unit Burr-XII distribution. The basic statistical properties of the newly defined distribution are studied. Parameters estimation is dealt and different estimation methods are assessed through two simulation studies. A new quantile regression model based on the proposed distribution is introduced. Applications of the proposed distribution and its regression model to real data sets show that the proposed models have better modeling capabilities than competing models.

On the Arcsecant Hyperbolic Normal Distribution. Properties, Quantile Regression Modeling and Applications

This work proposes a new distribution defined on the unit interval. It is obtained by a novel transformation of a normal random variable involving the hyperbolic secant function and its inverse. The use of such a function in distribution theory has not received much attention in the literature, and may be of interest for theoretical and practical purposes. Basic statistical properties of the newly defined distribution are derived, including moments, skewness, kurtosis and order statistics. For the related model, the parametric estimation is examined through different methods. We assess the performance of the obtained estimates by two complementary simulation studies. Also, the quantile regression model based on the proposed distribution is introduced. Applications to three real datasets show that the proposed models are quite competitive in comparison to well-established models.

A New Family of Extended Lindley Models: Properties, Estimation and Applications

There are many proposed life models in the literature, based on Lindley distribution. In this paper, a unified approach is used to derive a general form for these life models. The present generalization greatly simplifies the derivation of new life distributions and significantly increases the number of lifetime models available for testing and fitting life data sets for biological, engineering, and other fields of life. Several distributions based on the disparity of the underlying weights of Lindley are shown to be special cases of these forms. Some basic statistical properties and reliability functions are derived for the general forms. In addition, comparisons among various forms are investigated. Moreover, the power distribution of this generalization has also been considered. Maximum likelihood estimator for complete and right-censored data has been discussed and in simulation studies, the efficiency and behavior of it have been investigated. Finally, the proposed models have been fit to some data sets.

Random coefficients integer-valued threshold autoregressive processes driven by logistic regression

In this article, we introduce a new random coefficients self-exciting threshold integer-valued autoregressive process. The autoregressive coefficients are driven by a logistic regression structure, so that the explanatory variables can be included. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares and conditional maximum likelihood estimators, as well as the asymptotic properties of the estimators, are discussed. The nonlinearity test of the model and existence test of explanatory variables are also addressed. As an illustration, we evaluate our estimates through a simulation study. Finally, we apply our method to the data sets of sexual offences in Ballina, New South Wales (NSW), Australia, with two covariates of temperature and drug offences. The result reveals that the proposed model fits the data sets well.

A New Unit Distribution Based On The Unbounded Johnson Distribution Rule: The Unit Johnson SU Distribution

This paper proposes a new probability distribution, which belongs a member of the exponential family, defined on (0,1) unit interval. The new unit model has been defined by relation of a random variable defined on unbounded interval with respect to standard logistic function. Some basic statistical properties of newly defined distribution are derived and studied. The different estimation methods and some inferences for the model parameters have been derived. We assess the performance of the estimators of these estimation methods based on the three different simulation scenarios. The analysis of three real data examples which one is related to the coronavirus data, show better fit of proposed distribution than many known distributions on the unit interval under some comparing criteria.

Evaluation of social network conservation in historical areas of mountainous towns in Chongqing, China

Over recent decades, historical areas conservation has become an important strategy to improve urban competitiveness in the global economy. As shown in existing studies that the conservation of historical areas mainly focused on the physical environment, there is still room for the non-physical study, and researches on the social network conservation in mountainous historical areas are particularly insufficient. Therefore, this paper aims to establish an evaluation system which is helpful for the social network conservation of historical areas. The evaluation system is based on social network analysis and the information of social relationships gathered in field surveys using a specifically designed questionnaire method in four mountainous towns in Chongqing, China. And it was analyzed from three perspectives, i.e., by the basic statistical properties, condensate subgroup, and centrality. Then five analysis indicators were conceived, including density, lambda set, k-core, degree centrality, and betweenness centrality. The analysis results demonstrate that the social networks of the four towns show different indicators, which are respectively relevant to completeness degree, edge-relatedness level, local stability, structural balance, and concentrated trend of social relationships. Results from SNA modeling indicate that neighborhood residents of historical areas who have more stable and healthier social relationships are relatively not easily be destroyed. The results also illustrate that the social networks structure is influenced by the terrain, form, and function of historical areas, and the change of historical areas is caused by “individual-family-society”. Finally, the strategies guiding the social network conservation are put forward from two aspects. These findings suggest that the conservation and management of social network and aborigines in historical areas should be emphasized to increase the collective benefits and vitality.

Thermal fluctuations and boundary layer properties of turbulent natural convection inside open cavities of different dimensions heated from below

We report the experimental measurement of the temperature fluctuation in the vicinity of different zones of the thermal boundary layer in water-filled open cubic cavities heated from below and open at the top. The experiments are performed on the cubic cavity of aspect ratio 1 and lateral dimension 30 mm; the results of our previously reported open cubic cavities of aspect ratio 1 and lateral dimensions (120 mm and 240 mm) are also considered here. The transient nature of the temperature has been measured from the temperature–time series recorded across the central axis of the cavity at different vertical positions z from the heated bottom plate. The Prandtl number and Rayleigh number ranges reported in this paper are 4 ≤ Pr ≤ 6 and 105 ≤ Ra ≤ 109, respectively. The different basic statistical properties, of temperature fluctuation such as mean temperature, root mean square, and probability density function, are studied and discussed. The power-law of power spectral density of the temperature fluctuations at different regions of the thermal boundary layer is studied, and the different roles of rate are compared with the previously established theories and models. The validity criteria for the Oberbeck–Boussinesq approximation are fulfilled. The trend of the dimensionless Nusselt number (Nu) representing the global convective heat transfer is obtained and discussed. We also study the variation in Raδth−1 3 for the heat transfer representation in the range of 0.04–0.24, where δth is the boundary layer thickness.

Synthetic catalog of black holes in the Milky Way

Aims. We present an open-access database that includes a synthetic catalog of black holes (BHs) in the Milky Way, divided by the components disk, bulge, and halo. Methods. To calculate the evolution of single and binary stars, we used the updated population synthesis code StarTrack. We applied a new model of the star formation history and chemical evolution of Galactic disk, bulge, and halo that was synthesized from observational and theoretical data. This model can be easily employed for other studies of population evolution. Results. We find that at the current Milky Way (disk+bulge+halo) contains about 1.2 × 108 single BHs with an average mass of about 14 M⊙, and 9.3 × 106 BHs in binary systems with an average mass of 19 M⊙. We present basic statistical properties of the BH population in three Galactic components such as the distributions of BH masses, velocities, or the numbers of BH binary systems in different evolutionary configurations. Conclusions. The metallicity of a stellar population has a significant effect on the final BH mass through the stellar winds. The most massive single BH in our simulation of 113 M⊙ originates from a merger of a BH and a helium star in a low-metallicity stellar environment in the Galactic halo. We constrain that only ∼0.006% of the total Galactic halo mass (including dark matter) can be hidden in the form of stellar origin BHs. These BHs cannot be detected by current observational surveys. We calculated the merger rates for current Galactic double compact objects (DCOs) for two considered common-envelope models: ∼3–81 Myr−1 for BH-BH, ∼1–9 Myr−1 for BH-neutron star (NS), and ∼14–59 Myr−1 for NS-NS systems. We show the evolution of the merger rates of DCOs since the formation of the Milky Way until the current moment with the new star formation model of the Galaxy.

Brain-related genes are specifically enriched with long phase 1 introns.

Intronic gene regions are mostly considered in the scope of gene expression regulation, such as alternative splicing. However, relations between basic statistical properties of introns are much rarely studied in detail, despite vast available data. Particularly, little is known regarding the relationship between the intron length and the intron phase. Intron phase distribution is significantly different at different intron length thresholds. In this study, we performed GO enrichment analysis of gene sets with a particular intron phase at varying intron length thresholds using a list of 13823 orthologous human-mouse gene pairs. We found a specific group of 153 genes with phase 1 introns longer than 50 kilobases that were specifically expressed in brain, functionally related to synaptic signaling, and strongly associated with schizophrenia and other mental disorders. We propose that the prevalence of long phase 1 introns arises from the presence of the signal peptide sequence and is connected with 1-1 exon shuffling.

Negative binomial improved second degree lindley distribution and its application

The objective of this paper is to introduce a new two parameter mixed negative binomial distribution, namely negative binomial-improved second degree Lindley(NB-ISL) distribution. This distribution is obtained by mixing the negative binomial distribution with the improved second degree Lindley distribution. Many mixed distributions have been used in the literature for modeling the over dispersed count data, which provide a better fit compared to the Poisson and negative binomial distribution. In addition, we present the basic statistical properties of the new distribution such as factorial moments, mean and variance and the behavior of mean, variance and coefficient of variation are also discussed. Parameter estimation is implemented by using maximum likelihood estimation method. The performance of the NB-ISL distribution is shown in practice by applying it on real data set and compare it with some well-known count distributions. The result shows that the negative binomial-improved second degree Lindley distribution provides a better fit compared to Poisson, negative binomial and negative binomial-Lindley distributions.

Inference for Two-Stage Sampling Designs

SummaryTwo-stage sampling designs are commonly used for household and health surveys. To produce reliable estimators with associated confidence intervals, some basic statistical properties like consistency and asymptotic normality of the Horvitz–Thompson estimator are desirable, along with the consistency of associated variance estimators. These properties have been mainly studied for single-stage sampling designs. In this work, we prove the consistency of the Horvitz–Thompson estimator and of associated variance estimators for a general class of two-stage sampling designs, under mild assumptions. We also study two-stage sampling with a large entropy sampling design at the first stage and prove that the Horvitz–Thompson estimator is asymptotically normally distributed through a coupling argument. When the first-stage sampling fraction is negligible, simplified variance estimators which do not require estimating the variance within the primary sampling units are proposed and shown to be consistent. An application to a panel for urban policy, which is the initial motivation for this work, is also presented.

A multinomial autoregressive model for finite-range time series of counts

In this paper, a multinomial autoregressive model for finite-range time series of counts is introduced to analyze the finite-range integer-valued data with more than two states. Basic probabilistic and statistical properties of the model are discussed. The related estimations of the parameters in proposed model are considered using conditional least squares (CLS), weighted conditional least squares (WCLS) and conditional maximum likelihood (CML) methods. The asymptotic properties of the estimators are established. Some simulation studies are conducted to verify the proposed procedure. A real example is analyzed to illustrate the advantages of our model.

The cosine geometric distribution with count data modeling

In this paper, a new two-parameter discrete distribution is introduced. It belongs to the family of the weighted geometric distribution (GD), with the feature of using a particular trigonometric weight. This configuration adds an oscillating property to the former GD which can be helpful in analyzing the data with over-dispersion, as developed in this study. First, we present the basic statistical properties of the new distribution, including the cumulative distribution function, hazard rate function and moment generating function. Estimation of the related model parameters is investigated using the maximum likelihood method. A simulation study is performed to illustrate the convergence of the estimators. Applications to two practical datasets are given to show that the new model performs at least as well as some competitors.

A new heavy-tailed distribution defined on the bounded interval: the logit slash distribution and its application

This paper proposes a new heavy-tailed and alternative slash type distribution on a bounded interval via a relation of a slash random variable with respect to the standard logistic function to model the real data set with skewed and high kurtosis which includes the outlier observation. Some basic statistical properties of the newly defined distribution are studied. We derive the maximum likelihood, least-square, and weighted least-square estimations of its parameters. We assess the performance of the estimators of these estimation methods by the simulation study. Moreover, an application to real data demonstrates that the proposed distribution can provide a better fit than well-known bounded distributions in the literature when the skewed data set with high kurtosis contains the outlier observations.

Optimal Control of Eye Movements During Visual Search

In this paper, we study the problem of an optimal oculomotor control during the execution of visual search tasks. We introduce a computational model of human eye movements, which takes into account various constraints of the human visual and oculomotor systems. In the model, the choice of the subsequent fixation location is posed as a problem of a stochastic optimal control, which relies on reinforcement learning methods. We show that if biological constraints are taken into account, the trajectories simulated under a learned policy share both basic statistical properties and a scaling behavior with human eye movements. We validated our model simulations with human psychophysical eye-tracking experiments.

On the theory of periodic multivariate INAR processes

In this paper a multivariate integer-valued autoregressive model of order one with periodic time-varying parameters, and driven by a periodic innovations sequence of independent random vectors is introduced and studied in detail. Emphasis is placed on models with periodic multivariate negative binomial innovations. Basic probabilistic and statistical properties of the novel model are discussed. Aiming to reduce computational burden arising from the use of the conditional maximum likelihood method, a composite likelihood-based approach is adopted. The performance of such method is compared with that of some traditional competitors, namely moment estimators and conditional maximum likelihood estimators. Forecasting is also addressed. Furthermore, an application to a real data set concerning the monthly number of fires in three counties in Portugal is presented.