<p><span>Rainfall intensity-duration-frequency (IDF) curves are required for the design of several water systems and protection works. These curves are typically generated from the station data by fitting a theoretical distribution either to the annual extremes (AMS) or partial extremes (PE) series. Nevertheless, two main problems arise: i) for generating intensity depth for high return periods, long time series are needed (more than 40 years). While this is the case mainly for daily recordings, for sub-hourly time series only few point measurements are available. ii) as the station data are only local measurements, there is a need for regionalization of the of IDF curves to ungauged locations. Thus, the aim of this study is to investigate the use of different data types and methods in generating reliable IDF curves for ungauged locations. </span></p><p><span>For this purpose, the available gauge data from the German Weather Service (DWD) in Germany are employed, which include: 5000 daily stations with more than 40 years available, 1100 sub-hourly (5min) recordings with observations period shorter than 20 years, and finally 89 sub-hourly (5min) recordings with 60-70 years of observations. Annual extremes are extracted for each location for different durations D=5, 10, 15, 30, 60, 120, 180, 240, 360, 720, 2880 minutes, and a Generalized Extreme Value (GEV) probability distribution is fitted to each duration level as well as across all duration levels by the methods of the L-moments and Maximum-Likelihood, in order to derive the intensity quantiles for the given return periods Ta=2, 10, 20 and 100 years. First, a disaggregation scheme to 5 min resolution is performed on the daily recordings in order to investigate if disaggregated daily data can be useful for the IDF estimation of sub-daily durations. Then, the rainfall extremes of short observations are corrected by a correlation-based augmentation method. Finally, as the extreme intensities and durations are co-dependent, a normalization of the AMS over all the durations is performed.</span></p><p><span>To evaluate the regionalization of the IDF curves to ungauged regions, three methods are investigated: i) flood index method ii) regionalization with normalization of extremes over the durations and ii) kriging interpolation (ordinary and external drift kriging) of local AMS quantiles or parameters of the fitted distribution. The performance of these regionalization techniques is then evaluated by cross-validation, where the local IDF from the long sub-hourly time series are considered the true reference. Based on the relative bias, rmse and correlation the best method is selected and used for the regionalization of the IDF curves in Germany. Different data products are fed in the regionalization methods to answer the following questions: are the disaggregated long time series useful in regionalizing sub-hourly IDF? Can space be traded for time (and vice versa) when regionalizing IDF? What is the best incorporation of different data sets for the regionalization of the IDF? Lastly, a bootstrap method is as well employed to account for the uncertainties in estimation intensity-duration extremes for the given return periods. </span></p>
Multivariate Behrens-Fisher Problem is a problem that deals with testing the equality of two means from multivariate normal distribution when the covariance matrices are unequal and unknown. However, there is no single procedure served as a better performing solution to this problem, Adebayo (2018). In this study effort is made in selecting five different existing procedures and examined their power and rate to which they control type I error using a different setting and conditions observed from previous studies. To overcome this problem a code was designed via R Statistical Software, to simulate random normal data and independently run 1000 times using MASS package in other to estimate the power and rate at which each procedure control type I error. The simulation result depicts that, in a setting when variance covariance matrices S1 > S2 associated with a sample sizes (n1 > n2) in Table 4.1, 4.2, 4.5, and 4.6, shows that, Adebayos’ procedure performed better but at a sample sizes (n1 = n2 and n1 < n2) Hotelling T2 is recommended in terms of power. For type I error rate where robustness and nominal level matters we found that under some settings none of the procedure maintained nominal level as revealed in Table 4.11 and 4.15. The results presented in Table 4.9 to 4.16 shows that when nominal level matters Krishnamoorthy came first, followed by Adebayos’, Yaos’, Johansons’ then Hotelling T2 were recommended in the sequentially under the settings used in this study.
The study aimed at investigating the effects of demographic parameters on both economic and population growth in Nigeria. Three models were employed in the study and results from model 1 depicted that economic growth has a positive effects to BR and negatively affected by DR, these results had demonstrated that increase in population growth in Nigeria is favorable to economic growth of the nation while death was found unfavorable to the economic growth in Nigeria. This result is an indication of the fact that Nigeria is not facing the problem of overpopulation; rather the capacities of Nigerian Government and responsible organizations to create a favorable economic environment by channeling the right resources into the right place. In the second model we also discovered that labor force was statistically significant with a P-value of 0.00328. Thus, model 3 regressed GDP, labor force, health expenditure and corruption perception on population growth. The results depicted that all, except health expenditure with 0.82552 P-value, are statistically significant. The results have shown the influence of economic growth, labour force and corruption on the growth of population in Nigeria. The data in this work were of two types from three different sources; National Bureau of Statistics (NBS), African Development Bank (ADB) and World Bank (WB), first part ranges from 1995 to 2018 and second part ranges from 1985 to 2018.
Gross Domestic Product GDP of any given country must also be one of the most difficult measures to predict due to its complexity while modelling. However, this study employed the used of Autoregressive Integrated Moving Average (ARIMA) model for Nigerian GDP 1960 to 2020 data obtained in World Bank database. In the study we found that first difference is insignificant, therefore, we alternatively used a log of the first difference and hence discovered that it is the most suitable model as compare with second difference, where ARIMA (2,1,2) was found with lowest information criteria under parameters estimate. The choosing model was used to forecast the Nigerian GDP using both in sample and out sample prediction method, where 80% of the data was used for training and yield an interesting good performing result with 94.41% accuracy while 20% of the data was presented for testing model (2,1,2) and forecasting.
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