On an exponential family

This paper considers a generalization of the exponential type distributions in the class of exponential families. A characterization and a method of generating an exponential family from a given family are given. In particular the generalized gamma, the generalized Poisson, the inverse Gaussian distributions belonging to this family are discussed. The approximations of the cumulative sums for the generalized gamma and the generalized Poisson by the Chi-square are considered. Some of the results are extended to the bivariate case.     

Forecasting demand for food in Libya—using confidence limits

Many developing countries are not self-sufficient in food production and they depend on food imports. In order to plan imports well in advance, the demand for food must be forecasted. If the forecasts are too low, the people suffer. On the other hand if the forecasts are too high—the food being a perishable commodity—resources of the country are wasted. The Food and Agricultural Organization of the United Nations (FAO) undertakes such forecasts occasionally. The FAO however links the food consumption to the income of a country and then just assume future income. Such forecasts have no scientific validity and could both fall short or be grossly excessive. In this study, the methodologies of Time Series and Regression Analysis are combined to avoid any guesses. Then confidence intervals are built so that it can be stated, e.g. with 95 per cent confidence that a nation will not eat more than the amount specified. A comparison of costs is made and it is shown that a country can save millions of dollars through the method of statistical confidence limits rather than by adding arbitrary quantities to means and averages. Finally savings possible in some other developing countries, by adopting the proposed method, are tabulated.     

Generalized bent-cable methodology for changepoint data: a Bayesian approach

The choice of the model framework in a regression setting depends on the nature of the data. The focus of this study is on changepoint data, exhibiting three phases: incoming and outgoing, both of which are linear, joined by a curved transition. Bent-cable regression is an appealing statistical tool to characterize such trajectories, quantifying the nature of the transition between the two linear phases by modeling the transition as a quadratic phase with unknown width. We demonstrate that a quadratic function may not be appropriate to adequately describe many changepoint data. We then propose a generalization of the bent-cable model by relaxing the assumption of the quadratic bend. The properties of the generalized model are discussed and a Bayesian approach for inference is proposed. The generalized model is demonstrated with applications to three data sets taken from environmental science and economics. We also consider a comparison among the quadratic bent-cable, generalized bent-cable and piecewise linear models in terms of goodness of fit in analyzing both real-world and simulated data. This study suggests that the proposed generalization of the bent-cable model can be valuable in adequately describing changepoint data that exhibit either an abrupt or gradual transition over time.     

Randomized singular spectrum analysis for long time series

ABSTRACT

Singular spectrum analysis (SSA) is a relatively new method for time series analysis and comes as a non-parametric alternative to the classical methods. This methodology has proven to be effective in analysing non-stationary and complex time series since it is a non-parametric method and do not require the classical assumptions over the stationarity or over the normality of the residuals. Although SSA have proved to provide advantages over traditional methods, the challenges that arise when long time series are considered, make the standard SSA very demanding computationally and often not suitable. In this paper we propose the randomized SSA which is an alternative to SSA for long time series without losing the quality of the analysis. The SSA and the randomized SSA are compared in terms of quality of the model fit and forecasting, and computational time. This is done by using Monte Carlo simulations and real data about the daily prices of five of the major world commodities.     

Estimation and prediction in the presence of an outlier under Type-II censoring

A single-outlier data set containing some independent random variables is considered such that all of observations expect one have the same distribution. To describe the model of interested, a location-scale family of distributions is used and the estimation problem of the parameters is studied when the data are collected under Type-II censoring scheme. Moreover, three different predictors are presented to predict the censored order statistics. They are also compared regarding both of mean squared prediction error and Pitman's measure of closeness criteria. The role of outlier parameter as well as censorship rate is studied on performance of proposed estimator and predictors. The results of the paper are illustrated via a real data set. Finally, some conclusions are stated.     

Circular versions of systematic sampling in the presence of linear trend

In this paper, an alternative approach was employed and derived the explicit expressions of sample mean and its variance for the circular and the diagonal circular systematic schemes since these expressions were unavailable in the existing literature. The study also found the corrected estimator of population mean and average variance under super-population model for these scheme. It further revealed that the circular systematic sampling almost performed better than that of the diagonal circular systematic sampling in both linear and auto-correlated super-population models.     

Idiosyncratic Shocks and the Role of Nonconvexities in Plant and Aggregate Investment Dynamics

We study a model of lumpy investment wherein establishments face persistent shocks to common and plant‐specific productivity, and nonconvex adjustment costs lead them to pursue generalized (S, s) investment rules. We allow persistent heterogeneity in both capital and total factor productivity alongside low‐level investments exempt from adjustment costs to develop the first model consistent with the cross‐sectional distribution of establishment investment rates. Examining the implications of lumpy investment for aggregate dynamics in this setting, we find that they remain substantial when factor supply considerations are ignored, but are quantitatively irrelevant in general equilibrium. The substantial implications of general equilibrium extend beyond the dynamics of aggregate series. While the presence of idiosyncratic shocks makes the time‐averaged distribution of plant‐level investment rates largely invariant to market‐clearing movements in real wages and interest rates, we show that the dynamics of plants' investments differ sharply in their presence. Thus, model‐based estimations of capital adjustment costs involving panel data may be quite sensitive to the assumption about equilibrium. Our analysis also offers new insights about how nonconvex adjustment costs influence investment at the plant. When establishments face idiosyncratic productivity shocks consistent with existing estimates, we find that nonconvex costs do not cause lumpy investments, but act to eliminate them.     

External Assets as Predictors of Positive Emotions Among At‐Risk Youth in Malaysia

The present study is among the first to examine external assets as predictors of positive emotions among at‐risk youth. The study aims to examine the associations of external assets with positive emotions, determine external assets as a predictor of positive emotions in phase 1, and see if these predictors were consistently established in phase 2. At first contact, 403 participants from low‐income apartments in the suburbs of Kuala Lumpur, aged 13–25 years were asked to complete the 25 Developmental Assets, Malaysian version. The participants were also invited to participate in social activities organized by the PERMATA community. The same participants were approached four months later to examine the stability of measures. Multiple regression analysis revealed support is the most significant predictor of positive emotions at phase 1 whilst positive peer influence, family boundaries and caring neighborhood are the significant predictors at phase 2. Results suggested that the presence of other external assets can enhance the positive development of at‐risk youth, however, the support must be present to some extent in the first place.     

Women’s Strategic Responses to Intimate Partner Violence: A Study in a Rural Community of Bangladesh

The objective of this study was to explore women’s strategic responses to physical violence perpetrated by an intimate partner. Twenty women from a rural area of the Narshingdi district in the Dhaka division of Bangladesh who experienced physical violence at home participated in the study. Development of the interview protocol and data analysis were carried out by applying the consensual qualitative research (CQR) method. The results showed that several themes, such as women’s responses to intimate partner violence, arose from the data. First, coping strategies to pre‐violent events included three themes: (i) leaving the scene; (ii) trying to divert attention; and (iii) preparing to protest. Women’s strategic responses to violent events consisted of four themes: (i) leaving the scene; (ii) remaining silent or no giving response; (iii) seeking help from others; and (iv) protesting against the violence. Lastly, women’s strategic responses to post‐violent events consisted of three themes: (i) temporary abstinence; (ii) verbally abusive behavior to family members; and (iii) going to the parental home. Given the findings of this study, we conclude by suggesting that more work is needed to better understand effective strategies and to draw women to institutional services to prevent violence to a greater extent.