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Ratio Estimator of Population Mean in Simple Random Sampling
Sheryl Chebet Kosgey,
Leo Odongo
Issue:
Volume 11, Issue 6, November 2022
Pages:
167-174
Received:
9 October 2022
Accepted:
27 October 2022
Published:
4 November 2022
DOI:
10.11648/j.ajtas.20221106.11
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Abstract: This paper considers the problem of estimating the population mean in Simple Random Sampling. One key objective of any statistical estimation process is to find estimates of parameter of interest with more efficiency. It is well established that incorporating additional information in the estimation procedure gives enhanced estimators. Ratio estimation improves accuracy of the estimate of the population mean by incorporating prior information of a supporting variable that is highly associated with the main variable. This paper incorporates non-conventional measure (Tri-mean) with quartile deviation as they are not affected by outliers together with kurtosis coefficients and information on the sample size to develop an estimator with more precision. Using Taylor series expansion, the properties of the estimator are evaluated to first degree order. Further, the estimator’s properties are assessed by bias and mean squared error. Efficiency conditions are derived theoretically whereby the suggested estimator performs better than the prevailing estimators. To support the theoretical results, simulation and numerical studies are undertaken to assess efficiency of the suggested estimator over the existing estimators. Empirical analysis done through percentage relative efficiency indicate the suggested estimator performs better compared to the prevailing estimators. It is concluded that the suggested estimator is more efficient than the existing estimators.
Abstract: This paper considers the problem of estimating the population mean in Simple Random Sampling. One key objective of any statistical estimation process is to find estimates of parameter of interest with more efficiency. It is well established that incorporating additional information in the estimation procedure gives enhanced estimators. Ratio estima...
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Application of Progressive Type II Hybrid Censoring Scheme to Estimate Parameters of Kumaraswamy Distribution
Meymuna Shariff Jaffer,
Edward Gachangi Njenga,
George Kemboi Kirui Keitany
Issue:
Volume 11, Issue 6, November 2022
Pages:
175-183
Received:
22 October 2022
Accepted:
7 November 2022
Published:
11 November 2022
DOI:
10.11648/j.ajtas.20221106.12
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Abstract: This paper considers the Maximum Likelihood Estimators for Kumaraswamy distribution centered on progressive type II hybrid censoring scheme using the expectation maximization algorithm. Kumaraswamy distribution remains of keen consideration in disciplines such as economics, hydrology and survival analysis. To compare the performance of the attained maximum likelihood estimators of Kumaraswamy distribution expectation maximization algorithms is utilized as it is a convenient mechanism in manipulating incomplete data. The presentation of the maximum likelihood estimators via an expectation maximization algorithm is compared using three different amalgamations of censoring schemes. Simulation is utilized to contrast both precision and efficiency. The simulation outcome indicates that there is no notable estimation difference for the three censoring schemes. It also noted that an expectation maximization algorithm has a relatively efficient estimation aimed at Kumaraswamy distribution in progressive type II hybrid censoring scheme. Eventually, an illustration with real life data set is provided and it illustrates how maximum likelihood estimators works in practice under different censoring schemes. It is apparent from the observations made that the estimated values in scheme one is lesser than the other remaining two censoring schemes. It is greater in scheme three than scheme one and scheme two whenever, the three schemes are compared.
Abstract: This paper considers the Maximum Likelihood Estimators for Kumaraswamy distribution centered on progressive type II hybrid censoring scheme using the expectation maximization algorithm. Kumaraswamy distribution remains of keen consideration in disciplines such as economics, hydrology and survival analysis. To compare the performance of the attained...
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Comparative Analysis of Efficiency of Maximum Likelihood and Minimum Distance Estimation Techniques in Estimating Wind Distribution Parameters
Okumu Otieno Kevin,
Troon John Benedict,
Samuel Muthiga Nganga
Issue:
Volume 11, Issue 6, November 2022
Pages:
184-199
Received:
17 May 2022
Accepted:
16 June 2022
Published:
22 November 2022
DOI:
10.11648/j.ajtas.20221106.13
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Abstract: Wind distributions are essential in making predictions on chances of getting particular wind speeds and even the ability of particular areas producing specified wind power. However, the accuracy of the parameters in predicting the wind speeds and potential wind power depends on the robustness of the distribution parameters in the fitted wind distribution model. The robustness of the parameter however depends on the estimation technique employed in the estimation of the distribution parameters. Past studies have shown that various researchers have used methods such as Maximum Likelihood Estimation (MLE), Minimum Distance Estimation (MDE) methods and other methods such as Method of Moments and Least Square Estimation technique. Despite this, the studies have not been able to compare the efficiency of the techniques estimating parameters for wind distributions to determine which of the technique is more efficient. The study aimed at determining the most efficient method in estimating the distribution parameters for wind speed using the hourly wind data for Narok County in Kenya, from January 2016 to December 2018. The study fitted both 2 parameter and 3 parameter distributions for wind in the region using the two techniques and then compared the relative efficiency of the estimated parameters. The results showed that both 2 and 3 parameter distributions fitted using the Maximum Likelihood Estimation (MLE) technique had smaller relative efficiency compare to those of Minimum Distance Estimation (MDE) technique. In conclusion, the results were able to determine that MLE gave out more efficient parameters for wind distribution than the MDE technique. The study therefore, recommended the use of MLE technique in estimating the parameters of wind distributions.
Abstract: Wind distributions are essential in making predictions on chances of getting particular wind speeds and even the ability of particular areas producing specified wind power. However, the accuracy of the parameters in predicting the wind speeds and potential wind power depends on the robustness of the distribution parameters in the fitted wind distri...
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Analysis of Honey Value Chain: In Case of Mesela District, West Hararghe Zone, Ethiopia
Issue:
Volume 11, Issue 6, November 2022
Pages:
200-218
Received:
29 July 2022
Accepted:
13 September 2022
Published:
22 November 2022
DOI:
10.11648/j.ajtas.20221106.14
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Abstract: The purpose of this study was to analyze honey value chain with special emphasis to Mesela District, West Hararghe zone, Oromia, Ethiopia. The main objectives of the study were to identify the actors, activities, the distribution of costs and benefits among them and to identify factors affecting farmers’ participation in honey marketing and volume marketed in the study area. Both primary and secondary data were used and a total of 160 honey producing sample households from four potential honey producing kebeles of the District were surveyed. The result of regression analysis revealed that the beekeepers, collectors, processors, local brewery houses and retailers. Results from Heckman’s procedure shows among fourteen explanatory variables hypothesized to affect honey market participation decision sex of the household head, number of beehives owned, market information, household’s beekeeping experience, tropical livestock unit (TLU), and type of beehive used were found to be significant. Four variables, sex of the household head, number of beehives owned, credit access for honey production, type of beehive used were also found to be significantly influence the volume of honey sold by the participants of honey marketing. More evidence is needed on honey value chain before any generalization of the results can be made. In addition, the empirical tests were conducted only on 160 honey producer since 2015. Therefore, the results of the study cannot be assumed to extend beyond this group of honey producer to different study periods. The study might help the honey producer in addressing honey value chain raising awareness and capacity building of both farmers and District’s agricultural development agents through provision of appropriate training on how to manage bees and incorporate new technologies, and formation of beekeeper unions and cooperatives to address problems like lack of access to credit, market information and modern inputs are the actions to be taken to strengthen the sector’s contribution to the District’s development.
Abstract: The purpose of this study was to analyze honey value chain with special emphasis to Mesela District, West Hararghe zone, Oromia, Ethiopia. The main objectives of the study were to identify the actors, activities, the distribution of costs and benefits among them and to identify factors affecting farmers’ participation in honey marketing and volume ...
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Analysis of Volatility of Cryptocurrencies in the Global Market
Douglas Wangila Khamila,
Pius Kihara,
Levi Mbugua
Issue:
Volume 11, Issue 6, November 2022
Pages:
219-224
Received:
28 October 2022
Accepted:
16 November 2022
Published:
30 November 2022
DOI:
10.11648/j.ajtas.20221106.15
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Abstract: The motivation of this study was to analyze the volatility of Bitcoin, Ethereum, and Ripple cryptocurrencies in the global market. The weekly price and cryptocurrency trading datasets were outsourced from https.//Coinmarketcap.com. The period under study was from 1st February 2015 to 26th December 2021. Descriptive statistics for each cryptocurrency were analyzed and produced the following results. The mean for Ripple is 0.33, with a standard deviation of 0.39, a skewness of 1.97, and a kurtosis of 5.34 while the mean for Ethereum is 906.13, with a standard deviation of 1158.51, a skewness of 1.72 and kurtosis 1.8. The Mean for Bitcoin is 11242.34, standard deviation 15941.38, skewness 1.95, and kurtosis 2.67. This study was subjected to Garch Model analysis to determine the market volatility of Bitcoin, Ripple, and Ethereum cryptocurrencies. The analysis showed that ripple prices were constant from the years 2015 to 2017 low volatile then rose to high prices in the same year, the price variation with time was seen after 2017 to 2021, which means the prices were highly volatile. This suggested that the autocorrelation and seasonality of the structure of ripple cryptocurrency are not determinable. However, when data was subjected to compounding the return for ripple prices to check if there is any deviation in price variation through the study period, The result revealed that the highest volatility was presented in the year 2018. Ethereum price maintained a constant trend from 2018 to mid-2020 volatile and the prices increased with time to 2021 highly volatile as seen in figure 3. Bitcoin presented price variation with time as seen in figure 4, this shows a volatile market. By using Akaike Information Criterion was possible to identify the best Garch Models fitted to individual cryptocurrencies. This study has provided vital information to businesses, investors, and Governments to consider when making an informed decision regarding the type of cryptocurrencies to consider when making investment decisions, the price variability, and the volatility of cryptocurrencies in the market.
Abstract: The motivation of this study was to analyze the volatility of Bitcoin, Ethereum, and Ripple cryptocurrencies in the global market. The weekly price and cryptocurrency trading datasets were outsourced from https.//Coinmarketcap.com. The period under study was from 1st February 2015 to 26th December 2021. Descriptive statistics for each cryptocurrenc...
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Exponential Mean and Ratio-Types Estimators of Population Mean Using Moments Under Calibration Approach
Menakshi Pachori,
Neha Garg
Issue:
Volume 11, Issue 6, November 2022
Pages:
225-237
Received:
21 November 2022
Accepted:
13 December 2022
Published:
23 December 2022
DOI:
10.11648/j.ajtas.20221106.16
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Abstract: Calibration is a well-known technique for weight adjustment using various sets of constraints. This paper considers exponential ratio-type calibrated estimators for finite population mean using first three moments about the origin of the auxiliary variable in the calibration constraint under stratified random sampling. The exponential mean-type estimators for the second and third order moments are also suggested for the mentioned sampling scheme. When first three moments of the auxiliary variable are not known, then we use stratified double sampling scheme to estimate these moments. Thus, the result has been extended in the case of stratified double sampling and exponential mean-type and exponential ratio-type estimators have been developed using first three moments about the origin in the calibration constraints. The expression for mean squared error for the suggested estimators have been derived using the Taylor linearization method. For judging the performance of the proposed estimators, a simulation study has been carried out on two real datasets of MU284 population using R-software and their percentage root mean squared error (%RRMSE) and relative efficiency have been computed. The suggested estimators have been compared with the existing estimators given in the same setup and the new developed estimators are found to be more efficient than these estimators for the considered datasets.
Abstract: Calibration is a well-known technique for weight adjustment using various sets of constraints. This paper considers exponential ratio-type calibrated estimators for finite population mean using first three moments about the origin of the auxiliary variable in the calibration constraint under stratified random sampling. The exponential mean-type est...
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