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Mixed Seasonal and Subset Fourier Model with Seasonal Harmonics
Iberedem Aniefiok Iwok,
Murphy Dooga
Issue:
Volume 5, Issue 1, February 2017
Pages:
1-9
Received:
30 September 2016
Accepted:
13 October 2016
Published:
14 January 2017
Abstract: In this work, Box-Jenkins seasonal model was fitted to a temperature series and the assumption of model adequacy was found to be violated. Subset Fourier series with seasonal harmonics was introduced and added to the pure seasonal component that was found to be inadequate. This combination resulted in a mixed seasonal and subset Fourier model with seasonal harmonics. The mixed model was fitted to the data and was subjected to diagnostic checks. The tests revealed that the model was adequate. Comparative study was also carried out and the results showed that the mixed model performed better than the pure seasonal and the subset Fourier model.
Abstract: In this work, Box-Jenkins seasonal model was fitted to a temperature series and the assumption of model adequacy was found to be violated. Subset Fourier series with seasonal harmonics was introduced and added to the pure seasonal component that was found to be inadequate. This combination resulted in a mixed seasonal and subset Fourier model with ...
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The Best Spanning Tree of Heterogeneous Node Weighted Graphs
Issue:
Volume 5, Issue 1, February 2017
Pages:
10-14
Received:
16 January 2017
Published:
17 January 2017
Abstract: Minimum spanning tree theory has a wide application in many fields. But in many practical problems, we are often faced with the heterogeneous node weighted graph with both edge weight and node weight be considered. In this paper, we present the definition and the mathematical model of the best spanning tree, then raise an algorithm of the best spanning tree, finally, prove that the algorithm is effective in the best spanning tree problem through an application example.
Abstract: Minimum spanning tree theory has a wide application in many fields. But in many practical problems, we are often faced with the heterogeneous node weighted graph with both edge weight and node weight be considered. In this paper, we present the definition and the mathematical model of the best spanning tree, then raise an algorithm of the best span...
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An Optimal Split-Plot Design for Performing a Mixture-Process Experiment
Gladys Gakenia Njoroge,
Jemimah Ayuma Simbauni,
Joseph Arap Koske
Issue:
Volume 5, Issue 1, February 2017
Pages:
15-23
Received:
30 October 2016
Accepted:
21 November 2016
Published:
18 January 2017
Abstract: In many mixture-process experiments, restricted randomization occurs and split-plot designs are commonly employed to handle these situations. The objective of this study was to obtain an optimal split-plot design for performing a mixture-process experiment. A split-plot design composed of a combination of a simplex centroid design of three mixture components and a 22 factorial design for the process factors was assumed. Two alternative arrangements of design points in a split-plot design were compared. Design-Expert® version 10 software was used to construct I-and D-optimal split-plot designs. This study employed A-, D-, and E- optimality criteria to compare the efficiency of the constructed designs and fraction of design space plots were used to evaluate the prediction properties of the two designs. The arrangement, where there were more subplots than whole-plots was found to be more efficient and to give more precise parameter estimates in terms of A-, D- and E-optimality criteria. The I-optimal split-plot design was preferred since it had the capacity for better prediction properties and precision in the measurement of the coefficients. We thus recommend the employment of split-plot designs in experiments involving mixture formulations to measure the interaction effects of both the mixture components and the processing conditions. In cases where precision of the results is more desirable on the mixtures as well as where the mixture blends are more than the sets of process conditions, we recommend that the mixture experiment be set up at each of the points of a factorial design. In situations where the interest is on prediction aspects of the system, we recommend the I-optimal split-plot design to be employed since it has low prediction variance in much of the design space and also gives reasonably precise parameter estimates.
Abstract: In many mixture-process experiments, restricted randomization occurs and split-plot designs are commonly employed to handle these situations. The objective of this study was to obtain an optimal split-plot design for performing a mixture-process experiment. A split-plot design composed of a combination of a simplex centroid design of three mixture ...
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A Trinomial Probability Model for Occurrences of Stock Price Change: Evidence from Dhaka Stock Exchange
Md. Zahirul Islam,
Shakil Ahmad
Issue:
Volume 5, Issue 1, February 2017
Pages:
24-30
Received:
8 December 2016
Accepted:
19 December 2016
Published:
18 January 2017
Abstract: This paper is concerned with modeling the occurrences of stock price uncertainty of Dhaka Stock Exchange. Daily closing prices of three different banks are selected for analysis. This report focuses on the overall condition of the stock market to find out the amount of probability of uncertainty of occurrences by analytically chosen model to the financial data of Banking Sector (leading three Banks of Bangladesh: AB Bank, City Bank and National Bank). Various popular variability-forecasting models with techniques of measuring and evaluating performance of forecasting were reviewed. In this research, a trinomial probability distribution model is fitted considering the outcome (closing price) of a stock (per day) such as low, unchanged and high for the quoted three banks. Maximum likelihood estimations are derived for estimating the parameters of the model. To check the model acceptability chi-square goodness-of-fit test is conducted. It is found that the probability of occurrences of unchanged price for AB bank is low (0.014). On the other hand the probability of occurrence of high and low price are high (0.478 and 0.508) and these probabilities are almost same for the other banks (City and National bank).
Abstract: This paper is concerned with modeling the occurrences of stock price uncertainty of Dhaka Stock Exchange. Daily closing prices of three different banks are selected for analysis. This report focuses on the overall condition of the stock market to find out the amount of probability of uncertainty of occurrences by analytically chosen model to the fi...
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Hydromagnetic Turbulent Flow Between Two Parallel Infinite Plates
Kennedy John Mwangi Karimi,
Dickson Kande Kinyua
Issue:
Volume 5, Issue 1, February 2017
Pages:
31-40
Received:
28 September 2016
Accepted:
10 November 2016
Published:
21 January 2017
Abstract: In this study we shall investigate hydromagnetic turbulent unsteady flow of an incompressible electrically conducting fluid between two parallel infinite plates. The flow variables such as velocity and thermodynamic properties at every point of fluid vary with respect to time. The effect of an applied transverse magnetic field normal to the main flow direction on the dynamic behavior of the fluid when the lower plate is stationary and the upper plate is impulsively started in opposite direction at constant velocity shall be investigated. Further, we shall investigate how the various parameters such as Peclet Number and Eckert Number affect the flow; in particular, velocity and temperature profiles. A finite difference method shall be used to solve the coupled non-liner and dimensionless partial differential equations governing this problem.
Abstract: In this study we shall investigate hydromagnetic turbulent unsteady flow of an incompressible electrically conducting fluid between two parallel infinite plates. The flow variables such as velocity and thermodynamic properties at every point of fluid vary with respect to time. The effect of an applied transverse magnetic field normal to the main fl...
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The American Statistical Association (ASA) Statement of 2016 on Statistical Significance and P-value: A Critical Thought
Issue:
Volume 5, Issue 1, February 2017
Pages:
41-48
Received:
6 December 2016
Accepted:
4 January 2017
Published:
24 January 2017
Abstract: A study on American Statistical Association (ASA) policy statement on statistical significance testing and p-value of 2016 was carried out in Tanzania. The purpose of the study was to explore the feelings and reactions of university statistics tutors towards the American Statistical Association policy statement on statistical significance testing and p-value of 2016. A sample of 9 statistics tutors from different disciplines were selected from public and private universities via heterogeneous purposive sampling to participate in the study. Respondents had mixed feelings towards ASA policy statement of 2016. The ASA policy statement was criticized for being shallow in depth, subjective and failing to answer the core problems raised against the use of Null Hypothesis Significance Testing (NHST) and p-value. The ASA policy statement was dismissed as a non event with nothing new to offer. However, despite being shallow, the ASA policy on NHST and p-value is likely to trigger a health debate on the shortfalls of NHST and p-value and the debate will eventually lead to a breakthrough.
Abstract: A study on American Statistical Association (ASA) policy statement on statistical significance testing and p-value of 2016 was carried out in Tanzania. The purpose of the study was to explore the feelings and reactions of university statistics tutors towards the American Statistical Association policy statement on statistical significance testing a...
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Construction of Some Resolvable t-designs
Issue:
Volume 5, Issue 1, February 2017
Pages:
49-53
Received:
20 July 2016
Accepted:
8 August 2016
Published:
22 February 2017
Abstract: The A t-design is a generation of balanced incomplete block design (BIBD) where λ is not restricted to the blocks in which a pair of treatments occurs but to the number of blocks in which any t treatments (t = 2,3…) occurs. The problem of finding all parameters (t, v, k, λt) for which t-(v, k, λt) design exists is a long standing unsolved problem especially with λ=1 (Steiner System) as no Steiner t-designs are known for t ≥ 6 when v > k. In this study t-design is constructed by relating known BIB designs, combinatorial designs and algebraic structures with t-designs. Additionally, an alternative approach for the construction of t-designs that provides a unified framework is also presented.
Abstract: The A t-design is a generation of balanced incomplete block design (BIBD) where λ is not restricted to the blocks in which a pair of treatments occurs but to the number of blocks in which any t treatments (t = 2,3…) occurs. The problem of finding all parameters (t, v, k, λt) for which t-(v, k, λt) design exists is a long standing unsolved problem e...
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Prediction and Trends of Rainfall Variability over Bangladesh
Mohammad Anisur Rahman,
Sunny Mohammed Mostafa Kamal,
Mohammad Maruf Billah
Issue:
Volume 5, Issue 1, February 2017
Pages:
54-59
Received:
3 January 2017
Accepted:
19 January 2017
Published:
1 March 2017
Abstract: Rainfall is one of the most common natural disasters in Bangladesh which rigorously affect agro-based economy and people’s livelihood in almost every year. The main objective of this study is to examine the variation, prediction and trend of rainfall in Bangladesh. The data for this study have been extracted from the Bangladesh Meteorological Department (BMD). Data used in this study were collected from 31 rain gauge stations located in different parts of the country for a period of 40 years (1975-2014). Linear regression model is used to understand the variation, trend and prediction of rainfall for annual and various climatic seasons such as pre-monsoon, monsoon, post-monsoon and winter. We also estimated mean rainfall with standard deviation of pre-monsoon, monsoon, post-monsoon and winter. Finding reveals that, the trends of mean rainfall of annual, pre-monsoon and winter have decreased, whereas rainfall remained unchanged in monsoon season and has increased in post-monsoon. Data predicts lesser rainfall in the period 1975, 1989, 1992, 1994, 2004, 2009, 2012, 2013 and 2014 years. These results indicate lesser precipitation in future over Bangladesh. The predicted rainfall amount from the best fitted model was compared with the observed data. The predicted values show reasonably good result. Thus the model can be used for future rainfall prediction. It is expected that this long term prediction will help the decision makers in efficient scheduling of flood prediction, urban planning, and rainwater harvesting and crop management. Classification of rainfalls in a systematic way is therefore critical in order to take necessary actions toward drought mitigation and sustainable development.
Abstract: Rainfall is one of the most common natural disasters in Bangladesh which rigorously affect agro-based economy and people’s livelihood in almost every year. The main objective of this study is to examine the variation, prediction and trend of rainfall in Bangladesh. The data for this study have been extracted from the Bangladesh Meteorological Depar...
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