Journal of Data Science

This study aims to compare various quantitative models to forecast monthly foreign tourist arrivals (FTAs) to India. The models which are considered here include vector error correction (VEC) model, Naive I and Naive II models, seasonal autoregressive integrated moving average (SARIMA) model and Grey models. A model based on combination of single forecast values using simple average (SA) method has also been applied. The forecasting performance of these models have been compared under mean absolute percentage error (MAPE) and U-statistic (Ustat) criteria. Empirical findings suggest that the combination model gives better forecast of FTAs to India relative to other individual time series models considered here.

Abstract: Simulation studies are important statistical tools used to inves-tigate the performance, properties and adequacy of statistical models. The simulation of right censored time-to-event data involves the generation of two independent survival distributions, where the rst distribution repre-sents the uncensored survival times and the second distribution represents the censoring mechanism. In this brief report we discuss how we can make it so that the percentage of censored data is previously de ned. The described method was used to generate data from a Weibull distribution, but it can be adapted to any other lifetime distribution. We further presented an R code function for generating random samples, considering the proposed approach.

Analysing seasonality in count time series is an essential application of statistics to predict phenomena in different fields like economics, agriculture, healthcare, environment, and climatic change. However, the information in the existing literature is scarce regarding the performances of relevant statistical models. This study provides the Yule-Walker (Y-W), Conditional Least Squares (CLS), and Maximum Likelihood Estimation (MLE) for First-order Non-negative Integer-valued Autoregressive, INAR(1), process with Poisson innovations with different monthly means. The performance of Y-W, CLS, and MLE are assessed by the Monte Carlo simulation method. The performance of this model is compared with another seasonal INAR(1) model by reproducing the monthly number of rainy days in the Blackwater River watershed located in coastal Virginia. Two forecast-coherent methods in terms of mode and probability function are applied to make predictions. The models’ performances are assessed using the Root Mean Square Error and Index of Agreement criteria. The results reveal the similar performance of Y-W, CLS, and MLE for estimating the parameters of data sets with larger sample size and values of α close to unite root. Moreover, the results indicate that INAR(1) with different monthly Poisson innovations is more appropriate for modelling and predicting seasonal count time series.

Abstract: Medical data and biomedical studies are often imbalanced with a majority of observations coming from healthy or normal subjects. In the presence of such imbalances, agreement among multiple raters based on Fleiss’ Kappa (FK) produces counterintuitive results. Simulations suggest that the degree of FK’s misrepresentation of the observed agreement may be directly related to the degree of imbalance in the data. We propose a new method for evaluating agreement among multiple raters that is not affected by imbalances, A-Kappa (AK). Performance of AK and FK is compared by simulating various degrees of imbalance and illustrate the use of the proposed method with real data. The proposed index of agreement may provide some insight by relating its magnitude to a probability scale. Existing indices are interpreted arbitrarily. This new method not only provides a measure of overall agreement but also provides an agreement index on an individual item. Computation of both AK and FK may further shed light into the data and be useful in the interpretation and presenting the results.

In this paper we use the maximum likelihood (ML) and the modified maximum likelihood (MML) methods to estimate the unknown parameters of the inverse Weibull (IW) distribution as well as the corresponding approximate confidence intervals. The estimates of the unknown parameters are obtained based on two sampling schemes, namely, simple random sampling (SRS) and ranked set sampling (RSS). Comparison between the different proposed estimators is made through simulation via their mean square errors (MSE), Pitman nearness probability (PN) and confidence length.

Abstract:In this paper we propose a new five parameter bivariate distribution obtained by taking geometric maximum of generalized exponential distributions. Several properties of this new bivariate distribution and its marginals have been investigated. It is observed that the maximum likelihood estimators of the unknown parameters cannot be obtained in closed form. Five non-linear equations need to be solved simultaneously to compute the maximum likelihood estimators of the unknown parameters. We propose to use the EM algorithm to compute the maximum likelihood estimators of the unknown parameters, and it is computationally quite tractable. We performed extensive simulations study to see the effectiveness of the proposed algorithm, and the performance is quite satisfactory. We analyze one data set for illustrative purposes. Finally we propose some open problems.

Abstract: Loss of household income and purchasing power are shown to have broad and negative societal effects. The economic anxiety accompanying this loss has its strongest impact on consumer demand, which is the major factor in a nation’s gross domestic product (GDP). Negative effects of economic anxiety are also found on the propensity to vote, political trust, societal satisfaction, and the quality of life. These effects were verified in a cross national sample from the fifth round of the European Social Survey. Simple regression of the true value of consumer demand, etc. on the true value of economic anxiety is made possible by an estimate of the reliability of our economic-anxiety score (cf. Bechtel, 2010; 2011; 2012). This reliability estimate corrects the regression slope of each societal variable for measurement error in the anxiety score.

Marshall and Olkin (1997) introduced a general method for obtaining more flexible distributions by adding a new parameter to an existing one, called the Marshall-Olkin family of distributions. We introduce a new class of distributions called the Marshall - Olkin Log-Logistic Extended Weibull (MOLLEW) family of distributions. Its mathematical and statistical properties including the quantile function hazard rate functions, moments, conditional moments, moment generating function are presented. Mean deviations, Lorenz and Bonferroni curves, R´enyi entropy and the distribution of the order statistics are given. The Maximum likelihood estimation technique is used to estimate the model parameters and a special distribution called the Marshall-Olkin Log Logistic Weibull (MOLLW) distribution is studied, and its mathematical and statistical properties explored. Applications and usefulness of the proposed distribution is illustrated by real datasets.

This paper proposes a new asymptotically valid stationary bootstrap procedure to obtain multivariate forecast densities in unrestricted vector autoregressive models. The proposed method is not based on either backward or forward representations, so it can be used for both Gaussian and non-Gaussian models. Also, it is computationally more efficient compared to the available resampling methods. The finite sample performance of the proposed method is illustrated by extensive Monte Carlo studies as well as a real-data example. Our records reveal that the proposed method is a good competitor or even better than the existing methods based on backward and/or forward representations.

Abstract: Suppose that an order restriction is imposed among several means in time series. We are interested in testing the homogeneity of these unknown means under this restriction. In the present paper, a test based on the isotonic regression is done for monotonic ordered means in time series with stationary process and short range dependent sequences errors. A test statistic is proposed using the penalized likelihood ratio (PLR) approach. Since the asymptotic null distribution of test statistic is complicated, its critical values are computed by using Monte Carlo simulation method for some values of sample sizes at different significance levels. The power study of our test statistic is provided which is more powerful than that of the test proposed by Brillinger (1989). Finally, to show the application of the proposed test, it is applied to real dataset contains monthly Iran rainfall records.