Raw and Central Moments of a Variety of Generalized Beta-Binomial Distributions via Stirling Numbers
Abstract: In this article, we consider the construction of various compound Binomials by mixing the success parameter with generalized Beta distributions within the unit interval. We then proceed to calculate the moments of the derived mixtures using Stirling numbers of the second kind.
Keywords: Binomial mixtures, Central moments, Factorial moments, Generalized Beta distributions, Raw moments, Stirling numbers.
Pages: 655 – 674 | Full PDF Paper
Charles Leyeka Lufumpa, Marc Koffi Kouakou, Désiré Kouamé Kanga
The study looks at the responses of African households of different income levels to changes in their incomes and prices of the commodities they consume. The study utilizes data on prices collected by the African Development Bank through its 2011 international comparison program implemented in 50 African countries. The data was mostly collected on a monthly basis over a period of 15 months ranging from January 2011 to march 2012. The data covered 12 broad consumption item groups and over 1,036 products in 50 African countries that are classified in two groups: (i) the low income group with per capita income levels of under US $3,115 and (ii) the higher income group of countries with per capita income levels above US $3,115.
The 12 broad consumption groups include: food and non-alcoholic beverages; alcoholic beverages, tobacco and narcotics; clothing and footwear; housing, water, electricity, gas and other fuels; furnishings, household equipment and routine household maintenance; health; transport; communication; recreation and culture; education; restaurants and hotels; miscellaneous goods and services and net purchases abroad. The food category, which includes staples such as maize, bread and rice, comprises about a third of the items and approximately half of the consumption expenditure by households across Africa.
The study utilizes a two-stage cross-country demand model to estimate the aggregate demand systems for the broad consumption categories as well as the food sub-category. In the first stage of estimation, an aggregate demand system is generated using the Florida preference independence model. In the second stage, the Florida Slutsky model is used to generate a demand system for the food sub-category. The own price and income elasticities were computed using the procedure and formula outlined by Seale et al. (2003).
The study confirms that “food & non-alcoholic beverages” and “clothing and footwear” are necessary consumption items for African households. All other consumption categories, including education, are deemed as luxuries. Overall, the study shows that when total expenditure on all categories of goods and services increases by 1%, African households will tend to decrease their budget share for food by an average of 17.81 basis points in low income countries and 25.65 basis points in higher income countries.
In addition, “bread and cereals”, “fish”, “oils and fats” and “other food” are expenditure inelastic. In other words, an increase in the prices of these items results in an increase in total expenditure on each of these items. At the same level of income, households reallocate their budgets by reducing the consumption of other consumption categories (including on education and health) in preference for food, non-alcoholic beverages, clothing and footwear. This information on household consumption patterns and how they are affected by changes in household incomes and in the prices of goods and services in the economy can be helpful in informing public policies, especially those aimed at safeguarding the welfare of poor and marginalized households most affected by changes in price and income levels. Ensuring price stability for items that comprise the majority of the poor’s consumption baskets could go a long way in enhancing food security and household welfare.
Keywords: Consumption, two-stage cross-country demand model, food demand, elasticity, International Comparison Program.
Pages: 675 – 700 | Full PDF Paper
Abstract: In this paper, a relationship between two problems of manufacturing process planning with an unstable (fluctuating) sequence of raw materials supply is considered. The first problem is a problem of smoothing of the initial sequence using a stock of limited volume for raw materials. This problem is stated and solved as a problem of convex programming subject to constraints produced by the presence of the stock. The second problem (which is not classical) is to find such a plan that satisfies the constraints and has the least number of changes of manufacturing process intensity. It is shown that the optimal plan to the first problem may be a solution to the second problem under certain conditions, in general case it gives the possibility to determine a lower bound of changes for each feasible plan.
Keywords: smoothing, convex programming, active constraints, number of changes.
Pages: 701 – 713 | Full PDF Paper
Assist. Prof. Dr. Ahlam Ahmed Juma, Hala Muthanna Mohammed
The Forecasting of the time series of subjects that received attention especially effective role in contributing to the building plans for the future in all areas of life, including industrial, commercial, agricultural and other, As there were many methods of time series is the most important models developed worlds Box & Jenkins in 1970 and through the development of a methodology in the study and analysis of Autoregressive Integrated Moving Average Models ARIMA (p, d, q).
The research aims to the forecasting using linear time series and reaching a the best model can Predictable through, it was used non- seasonal Box-Jenkins models and were used the time series of the total area and the yield and production of cotton crop in Iraq for the period (1941 – 2011) was included forecasting future years (2012-2016).
Pages: 714 – 729 | Full PDF Paper
Brijesh P. Singh, Shweta Dixit and Upasana Shukla
Abstract: In this paper an attempt has been made to propose an alternative of truncated and intervened Poisson distribution, having two parameters and named as Bounded Poisson (BP) distribution. To estimate the parameters, method of moment and first cell frequency method have been used. To check the suitability of the model it has been applied on real data set used by Dahiya et al. (1973). Proposed model provides a good fitting to the data under consideration.
Pages: 730 – 740 | Full PDF Paper