Aim To quantitatively study three characteristics of the Weibull distribution. Methods Theoritical analysis of the three characteristics of parameters of the Weibull distribution was done and mathematics software wa...Aim To quantitatively study three characteristics of the Weibull distribution. Methods Theoritical analysis of the three characteristics of parameters of the Weibull distribution was done and mathematics software was used to make some chart analysis. Results 17 equations and 7 figures were made. Conclusion Under the standard form, the class of the Weibull probable density founction(pdf) curves appear double peak shape. Under the standard form, the maximum value point curve of the Weibull pdf takes line t =0 and t=1 as asymptotes. When β = 3 30-3 40, the Weibull distribution is the most similar to the normal distribution.展开更多
In this paper, we consider the construction of the approximate profile-</span><span style="font-family:""> </span><span style="font-family:Verdana;">likelihood confiden...In this paper, we consider the construction of the approximate profile-</span><span style="font-family:""> </span><span style="font-family:Verdana;">likelihood confidence intervals for parameters of the 2-parameter Weibull distribution based on small type-2 censored samples. In previous research works, the traditional Wald method has been used to construct approximate confidence intervals for the 2-parameter Weibull distribution</span><span style="font-family:""> </span><span style="font-family:Verdana;">under type-2 censoring scheme. However, the Wald technique is based on normality assumption and thus may not produce accurate interval estimates for small samples. The profile-likelihood and Wald confidence intervals are constructed for the shape and scale parameters of the 2-parameter Weibull distribution based on simulated and real type-2 censored data, and are hence compared using confidence length and coverage probability.展开更多
1-year hourly wind speed data from two Burundian stations, namely Bujumbura and Muyinga, have been processed in this work to bring an efficient help for the planning and installation of wind energy conversion systems ...1-year hourly wind speed data from two Burundian stations, namely Bujumbura and Muyinga, have been processed in this work to bring an efficient help for the planning and installation of wind energy conversion systems (WECS) at those localities. Mean seasonal and diurnal variations of wind direction and wind shear exponent have been derived. Two-parameter Weibull probability density functions (PDFs) fitting the observed monthly and annual wind speed relative frequency distributions have been implemented. As shown through three complementary statistical tests, the fitting technique was very satisfactory. A wind resource analysis at 10 m above ground level (AGL) has led to a mean power density at Bujumbura which is almost thirteen fold higher than at Muyinga. The use of the empirical power law to extrapolate wind characteristics at heights from 150 to 350 m AGL has shown that energy potential of hilltops around Muyinga was only suitable for small, individual scale wind energy applications. At the opposite, wind energy potential of ridge-tops and hilltops around Bujumbura has been found suitable for medium and large scale electricity production. For that locality and at those heights, energy outputs and capacity factors (CF or C<sub>f</sub>) have been computed for ten selected wind turbines (WTs), together with costs of electricity (COE) using the present value of cost (PVC) method. Amongst those WTs, YDF-1500-87 and S95-2.1 MW have emerged as the best options for installation owing to their highest CF and lowest COE. Moreover, an analysis of those two quantities at monthly basis for YDF-1500-87 WT has led to its best performance in the dry season. Compared to the average present COE of household hydroelectricity consumption, results of this study have evidenced economical feasibility and benefit of WECS setting in selected Burundian sites in order to supplement traditional electricity sources.展开更多
The probability distribution analysis is per-formed for multi-timescale aerosol optical depth (AOD) using AErosol RObotic NETwork (AERONET) level 2.0 data.The maximum likelihood estimation is employed to determine the...The probability distribution analysis is per-formed for multi-timescale aerosol optical depth (AOD) using AErosol RObotic NETwork (AERONET) level 2.0 data.The maximum likelihood estimation is employed to determine the best-fit probability density function (PDF),and the statement that the fitting Weibull distribution will be light-tailed is proved true for these AOD samples.The best-fit PDF results for multi-site data show that the PDF of AOD samples with longer timescale in most sites tends to be stably represented by lognormal distribution,while Weibull distribution is a better fit for AOD samples with short timescales.The reason for this difference is ana-lyzed through tail characteristics of the two distributions,and an indicator for the selection between Weibull and lognormal distributions is suggested and validated.The result of this research is helpful for determining the most accurate AOD statistics for a given site and a given time-scale and for validating the retrieved AOD through its PDF.展开更多
文摘Aim To quantitatively study three characteristics of the Weibull distribution. Methods Theoritical analysis of the three characteristics of parameters of the Weibull distribution was done and mathematics software was used to make some chart analysis. Results 17 equations and 7 figures were made. Conclusion Under the standard form, the class of the Weibull probable density founction(pdf) curves appear double peak shape. Under the standard form, the maximum value point curve of the Weibull pdf takes line t =0 and t=1 as asymptotes. When β = 3 30-3 40, the Weibull distribution is the most similar to the normal distribution.
文摘In this paper, we consider the construction of the approximate profile-</span><span style="font-family:""> </span><span style="font-family:Verdana;">likelihood confidence intervals for parameters of the 2-parameter Weibull distribution based on small type-2 censored samples. In previous research works, the traditional Wald method has been used to construct approximate confidence intervals for the 2-parameter Weibull distribution</span><span style="font-family:""> </span><span style="font-family:Verdana;">under type-2 censoring scheme. However, the Wald technique is based on normality assumption and thus may not produce accurate interval estimates for small samples. The profile-likelihood and Wald confidence intervals are constructed for the shape and scale parameters of the 2-parameter Weibull distribution based on simulated and real type-2 censored data, and are hence compared using confidence length and coverage probability.
文摘1-year hourly wind speed data from two Burundian stations, namely Bujumbura and Muyinga, have been processed in this work to bring an efficient help for the planning and installation of wind energy conversion systems (WECS) at those localities. Mean seasonal and diurnal variations of wind direction and wind shear exponent have been derived. Two-parameter Weibull probability density functions (PDFs) fitting the observed monthly and annual wind speed relative frequency distributions have been implemented. As shown through three complementary statistical tests, the fitting technique was very satisfactory. A wind resource analysis at 10 m above ground level (AGL) has led to a mean power density at Bujumbura which is almost thirteen fold higher than at Muyinga. The use of the empirical power law to extrapolate wind characteristics at heights from 150 to 350 m AGL has shown that energy potential of hilltops around Muyinga was only suitable for small, individual scale wind energy applications. At the opposite, wind energy potential of ridge-tops and hilltops around Bujumbura has been found suitable for medium and large scale electricity production. For that locality and at those heights, energy outputs and capacity factors (CF or C<sub>f</sub>) have been computed for ten selected wind turbines (WTs), together with costs of electricity (COE) using the present value of cost (PVC) method. Amongst those WTs, YDF-1500-87 and S95-2.1 MW have emerged as the best options for installation owing to their highest CF and lowest COE. Moreover, an analysis of those two quantities at monthly basis for YDF-1500-87 WT has led to its best performance in the dry season. Compared to the average present COE of household hydroelectricity consumption, results of this study have evidenced economical feasibility and benefit of WECS setting in selected Burundian sites in order to supplement traditional electricity sources.
基金supported by funds from the Chinese Global Change Research Program (Grant No.2010CB951804)the National Natural Science Foundation of China (Grant No.40830103)the China Postdoctoral Science Foundation (Grant No.20100480436)
文摘The probability distribution analysis is per-formed for multi-timescale aerosol optical depth (AOD) using AErosol RObotic NETwork (AERONET) level 2.0 data.The maximum likelihood estimation is employed to determine the best-fit probability density function (PDF),and the statement that the fitting Weibull distribution will be light-tailed is proved true for these AOD samples.The best-fit PDF results for multi-site data show that the PDF of AOD samples with longer timescale in most sites tends to be stably represented by lognormal distribution,while Weibull distribution is a better fit for AOD samples with short timescales.The reason for this difference is ana-lyzed through tail characteristics of the two distributions,and an indicator for the selection between Weibull and lognormal distributions is suggested and validated.The result of this research is helpful for determining the most accurate AOD statistics for a given site and a given time-scale and for validating the retrieved AOD through its PDF.
