Statistical Analysis Based on Adaptive Progressive Hybrid Censored Data From Lomax Distribution

In this article, we consider statistical inferences about the unknown parameters of the Lomax distribution basedon the Adaptive Type-II Progressive Hybrid censoring scheme, this scheme can save both the total test time and the cost induced by the failure of the units and increases the efficiency of statistical analysis. The estimation of the parameters is derived using the maximum likelihood (MLE) and the Bayesian procedures. The Bayesian estimators are obtained based on the symmetric and asymmetric loss functions. There are no explicit forms for the Bayesian estimators, therefore, we propose Lindley’s approximation method to compute the Bayesian estimators. A comparison between these estimators is provided by using extensive simulation. A real-life data example is provided to illustrate our proposed estimators.

A Berry-Esseen Bound for Nonlinear Statistics with Bounded Differences

In this paper, we obtain an explicit Berry-Esseen bound in the central limit theorem for nonlinear statistics with bounded differences. Some examples are provided as well.

S&P 500 Stock Price Prediction Using Technical, Fundamental and Text Data

We summarized both common and novel predictive models used for stock price prediction and combined them with technical indices, fundamental characteristics and text-based sentiment data to predict S&P stock prices. A 66.18% accuracy in S&P 500 index directional prediction and 62.09% accuracy in individual stock directional prediction was achieved by combining different machine learning models such as Random Forest and LSTM together into state-of-the-art ensemble models. The data we use contains weekly historical prices, finance reports, and text information from news items associated with 518 different common stocks issued by current and former S&P 500 large-cap companies, from January 1, 2000 to December 31, 2019. Our study's innovation includes utilizing deep language models to categorize and infer financial news item sentiment; fusing different models containing different combinations of variables and stocks to jointly make predictions; and overcoming the insufficient data problem for machine learning models in time series by using data across different stocks.

The Weibull Distribution: Reliability Characterization Based on Linear and Circular Consecutive Systems

Linear and circular consecutive models play a vital role to study the mechanical systems emerging in various fields including survival analysis, reliability theory, biological disciplines, and other lifetime sciences. As a result, analysis of reliability properties of consecutive k − out − of − n : F systems has gained a lot of attention in recent years from a theoretical and practical point of view. In the present article, we have studied some important stochastic and aging properties of residual lifetime of consecutive k − out − of − n : F systems under the condition n − k + 1, k ≤ n and all components of the system are working at time t. The mean residual lifetime (MRL) and its hazard rate function are proposed for the linear consecutive k − out − of − n : F (lin/con/k/n:F) and circular consecutive k − out − of − n : F (cir/con/k/n:F) systems. Furthermore, several mathematical properties of the proposed MRL are examined. Finally, the Weibull distribution with two parameters is used as an example to explain the theoretical results.

Infinity Substitute in Finding Exact Minimum of Total Weighted Tardiness in Tight-Tardy Progressive 1-machine Scheduling by Idling-free Preemptions

A job schedule ensuring the exact minimum of total weighted tardiness can be found with the respective integer linear programming problem model, in which the infinity showing that the respective states are either forbidden or impossible is substituted with a sufficiently great positive integer. An open question is whether the substitute can be selected so that the computation time would be decreased. Thus, it is ascertained that, whichever job lengths and its priority weights are, substituting the infinity with just “a sufficiently great positive integer” is never recommended. To decrease the computation time on average, it is strongly recommended to select the infinity substitute as multiple maximum over finite decision variable weights in the exact model. It is sufficient to take 2 to 5 such maxima as the infinity substitute. However, the shortened computation time is not guaranteed for solving a single or few scheduling problems. It is only an expected benefit, which builds up as a few hundred scheduling problems are solved at least.

Full Content-based Web Page Classification Methods by using Deep Neural Networks

The quality of the web page classification process has a huge impact on information retrieval systems. In this paper, we proposed to combine the results of text and image data classifiers to get an accurate representation of the web pages. To get and analyse the data we created the complicated classifier system with data miner, text classifier, and aggregator. The process of image and text data classification has been achieved by the deep learning models. In order to represent the common view onto the web pages, we proposed three aggregation techniques that combine the data from the classifiers.

A New One-parameter G Family of Compound Distributions: Copulas, Statistical Properties and Applications

This work introduces a new one-parameter compound G family. Relevant statistical properties are derived. The new density can be “asymmetric right skewed with one peak and a heavy tail”, “symmetric” and “left skewedwith one peak”. The new hazard function can be “upside-down”, “upside-down-constant”, “increasing”, “decreasing” and “decreasing-constant”. Many bivariate types have been also derived via different common copulas. The estimation of the model parameters is performed by maximum likelihood method. The usefulness and flexibility of the new family is illustrated by means of two real data sets.

Robust Filtering of Sequences with Periodically Stationary Multiplicative Seasonal Increments

We consider stochastic sequences with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. We solve the filtering problem for linear functionals constructed from unobserved values of a stochastic sequence of this type based on observations of the sequence with a periodically stationary noise sequence. For sequences with known matrices of spectral densities, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal filtering of the functionals. Formulas that determine the least favourable spectral densities and the minimax (robust) spectral characteristics of the optimal linear filtering of the functionals are proposed in the case where spectral densities of the sequence are not exactly known while some sets of admissible spectral densities are given.

Bayesian Estimation of The Ex-Gaussian Distribution

Fitting of the exponential modified Gaussian distribution to model reaction times and drawing conclusions from its estimated parameter values is one of the most popular method used in psychology. This paper aims to develop a Bayesian approach to estimate the parameters of the ex-Gaussian distribution. Since the chosen priors yield to posterior densities that are not of known form and that they are not always log-concave, we suggest to use the adaptive rejection Metropolis sampling method. Applications on simulated data and on real data are provided to compare this method to the standard maximum likelihood estimation method as well as the quantile maximum likelihood estimation. Results shows the effectiveness of the proposed Bayesian method by computing the root mean square error of the estimated parameters using the three methods.

A New Family of Continuous Distributions: Properties, Copulas and Real Life Data Modeling

A new family of distributions called the Kumaraswamy Rayleigh family is defied and studied. Some of its relevant statistical properties are derived. Many new bivariate type G families using the of Farlie-Gumbel-Morgenstern, modified Farlie-Gumbel-Morgenstern copula, Clayton copula and Renyi’s entropy copula are derived. The method of the maximum likelihood estimation is used. Some special models based on log-logistic, exponential, Weibull, Rayleigh, Pareto type II and Burr type X, Lindley distributions are presented and studied. Three dimensional skewness and kurtosis plots are presented. A graphical assessment is performed. Two real life applications to illustrate the flexibility, potentiality and importance of the new family is proposed.