| 1 |
Author(s):
Adejumo Oluwasegun Agbailu, Albert Seno, Onifade Oluwafemi Clement.
Page No : 1-9
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Kalman Filter Algorithm versus Other Methods of Estimating Missing Values: Time Series Evidence
Abstract
Ideally, we think data are carefully collected and have regular patterns with no missing values, but in reality, this does not always happen. This study examines four (4) methods—mean imputation (MI), median imputation (MDI), linear imputation (LI) and Kalman filter algorithm (KAL)—of estimating missing values in time series. The study utilized pairs of nine (9) simulated series; each pair constitutes “actual series” and “12% missingness series”. The three (3) sample sizes i.e. small (50), medium (200) and large (1000) were varied over the additive models linear, quadratic and exponential forms of trend. The 12% missingness series were estimated using MI, MDI, LI and KAL. The performances of the method were checked using the root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE), while the overall performances of the estimating methods were accessed using the average of the accuracy measures (RMSE, MAE and MAPE). The results of the average-accuracy measures show that KAL outperformed other methods (MI, MDI and LI) at the three sample sizes when the trend was linear; also, MDI outperformed other methods at the three (3) sample sizes when the trend was exponential. Furthermore, MI outperformed others at small and large sample sizes when the trend was quadratic. However, the Kalman filter algorithm proved better when the sample size was medium. Hence, KAL, MI and MDI methods are recommended to estimate missing data in time series when the trend is linear, quadratic and exponential respectively, until further study proves otherwise.
| 2 |
Author(s):
Jaja E.I., Iwundu M.P., Etuk E.H..
Page No : 10-24
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The Comparative study of CCD and MCCD in the presence of a missing design point
Abstract
The work constructed a modified central composite design from a rotatable central composite design augmented with seven center points adapted from the work of Wu and Li (2002). The comparison of the robustness of the CCD and MCCD to missing observation was investigated at various design points of factorial, axial and center points’ when the model is non-standard, using A-efficiency and the Losses associated. The results of the evaluations of the designs to missing observations are presented, and the MCCD is shown to be more A-optimal while the CCD is more robust and relatively A-efficient to a missing observation.
| 3 |
Author(s):
Jaja E.I., Etuk E.H., Iwundu M.P., Amos E..
Page No : 25-40
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Robustness of Central Composite Design and Modified Central Composite Design to a Missing Observation for Non-Standard Models
Abstract
Missing observations in an experimental design may lead to ambiguity in decision making thereby bringing an experiment to disrepute. Robustness, therefore, enables a process, not to break down in the presence of missing observations. This work constructed a modified central composite design (MCCD) from a four-variable central composite design (CCD) augmented with four center points using the leverage of a hat-matrix. The robustness of the CCD and MCCD were assessed when a design point is missing at the factorial, axial, and center points of the experiment, for a non-standard model, using the loss criterion, D-optimality, D-efficiency, and relative D-efficiency. When the designs are complete the MCCD shows higher D-efficiency and D-optimality for the non-standard model when compared to the CCD. In the absence of an observation from any of the designs, the CCD is found to be a more robust and efficient design compared to the MCCD as it has overall lower loss values at all the factors levels.
| 4 |
Author(s):
A.E. Anieting, E. I. Enang, C. E. Onwukwe.
Page No : 41-51
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Efficient Estimator for Population Mean in Stratified Double Sampling in the Presence of Nonresponse Using One Auxiliary Variable
Abstract
A modified form of the population mean estimator suggested by Anieting and Enang (2020) in stratified double sampling in the presence of nonresponse using a single auxiliary variable has been proposed. The Mean Squared Error (MSE) and the bias of the proposed estimator have been given using large sample approximation. The empirical study shows that the MSE of the suggested estimator is more efficient than all other existing estimators in the same scheme. Determination of the optimal values of the first and second phases samples has also been done
| 5 |
Author(s):
Eric U., Oti Michael O. Olusola, Francis C. Eze.
Page No : 52-65
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A Study of Properties and Applications of Gamma Distribution
Abstract
The gamma distribution is one of the continuous distributions; the distributions are very versatile and give useful presentations of many physical situations. They are perhaps the most applied statistical distribution in the area of reliability. In this paper, we present the study of properties and applications of gamma distribution to real life situations such as fitting the gamma distribution into data, burn-out time of electrical devices and reliability theory. The study employs the moment generating function approach and the special case of gamma distribution to show that the gamma distribution is a legitimate continuous probability distribution showing its characteristics.
| 6 |
Author(s):
O.K. Ogunbamike.
Page No : 66-87
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A New Approach on the Response of Non-Uniform Prestressed Timoshenko Beams on Elastic Foundation Subjected to Harmonic Loads
Abstract
The dynamic response of Timoshenko beam resting on an elastic foundation subjected to harmonic moving load using modal analysis (MA) is investigated. The method of MA was employed to obtain closed form solution to this class of dynamical system. In order to MA, accurate information is needed on the natural frequencies, mode shapes; orthogonality of the mode shapes a prior. A thorough literature survey reveals that the method has not been reported in existing literature to solve non-prestressed Timoshenko beam. Thus, we present complete information on how to use MA to derive the forced vibration responses of a simply thick beam subjected to harmonic moving loads. The effects of axial force and foundation parameter on the dynamic characteristics of the beams are studied and described in detail. In order to validate the accuracy of this method, we compare the frequency parameter with the existing literature which shows to compare favorably.
Keywords: Elastic foundation; Harmonic moving load; Modal analysis; Non-prestressed; Timoshenko beam.
| 7 |
Author(s):
Wiri Leneenadogo, Sibeate Pius U., Isaac Didi Essi.
Page No : 88-100
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Markov Switching Intercept Vector Autoregressive Model (MSI(2)-VAR(2)) of Nigeria Inflation Rate and Crude Oil Price (Using Views 11)
Abstract
To model inflation rate and crude oil prices, we used Markov Switching intercept heteroscedasticity Vector Autoregressive models. The data for this analysis was gathered from the Central Bank of Nigeria Statistical Bulletin monthly. The upward and downward movement in the series revealed by the time plot suggests that the series exhibit a regime-switching pattern: the period of expansion and contraction. The variable was stationary at first differences, the Augmented Dickey-Fuller test was used to screen for stationarity. The information criteria were used to test the number of regime and regime two were selected. Eight models were estimated for the MSI-VAR model. The best model was chosen based on the criterion of least information criterion, Markov-switching intercept heteroscedasticity – Vector Autoregressive model (MSIH(2)-VAR(2)) with AIC (8.596641) and SC (8.973119). The model was used to predict the series' values over a one-year cycle (12 months).
| 8 |
Author(s):
Okoli Christian Odilichukwu, Nwosu Dozie Felix, Osuji George Amaeze3, Nsiegbe Nelson Anayo.
Page No : 101-116
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On the Generalized Power Transformation of Left Truncated Normal Distribution
Abstract
In this study, we considered various transformation problems for a left-truncated normal distribution recently announced by several researchers and then possibly seek to establish a unified approach to such transformation problems for certain type of random variable and their associated probability density functions in the generalized setting. The results presented in this research, actually unify, improve and as well trivialized the results recently announced by these researchers in the literature, particularly for a random variable that follows a left-truncated normal distribution. Furthermore, we employed the concept of approximation theory to establish the existence of the optimal value y_max in the interval denoted by (σ_a,σ_b) ((σ_p,σ_q)) corresponding to the so-called interval of normality estimated by these authors in the literature using the Monte carol simulation method.
