We estimate the distribution of COVID-19 mortality(measured as daily deaths)from the start of the pandemic until July 31st,2022,for six European countries and the USA.We use the Pareto,the stretched exponential,the lo...We estimate the distribution of COVID-19 mortality(measured as daily deaths)from the start of the pandemic until July 31st,2022,for six European countries and the USA.We use the Pareto,the stretched exponential,the log-normal and the log-logistic distributions as well as mixtures of the log-normal and log-logistic distributions.The main results are that the Pareto does not describe well the data and that mixture distributions tend to offer a very good fit to the data.We also compute Value-at-Risk measures as well as mortality probabilities with our estimates.We also discuss the implications of our results and findings from the point of view of public health planning and modelling.展开更多
In this paper, a class of morphisms which have a kind of singularity weaker than normal crossing is considered. We construct the obstruction such that the so-called semi-stable log structures exists if and only if the...In this paper, a class of morphisms which have a kind of singularity weaker than normal crossing is considered. We construct the obstruction such that the so-called semi-stable log structures exists if and only if the obstruction vanishes. In the case of no power, if the obstruction vanishes, then the semi-stable log structure is unique up to a unique isomorphism. So we obtain a kind of canonical structure on this family of morphisms.展开更多
In this paper, we propose a log-normal linear model whose errors are first-order correlated, and suggest a two-stage method for the efficient estimation of the conditional mean of the response variable at the original...In this paper, we propose a log-normal linear model whose errors are first-order correlated, and suggest a two-stage method for the efficient estimation of the conditional mean of the response variable at the original scale. We obtain two estimators which minimize the asymptotic mean squared error （MM） and the asymptotic bias （MB）, respectively. Both the estimators are very easy to implement, and simulation studies show that they are perform better.展开更多
The relationship between RSSI (Received Signal Strength Indication) values and distance is the foundation and the key of ranging and positioning technologies in wireless sensor networks. Log-normal shadowing model (LN...The relationship between RSSI (Received Signal Strength Indication) values and distance is the foundation and the key of ranging and positioning technologies in wireless sensor networks. Log-normal shadowing model (LNSM), as a more general signal propagation model, can better describe the relationship between the RSSI value and distance, but the parameter of variance in LNSM is depended on experiences without self-adaptability. In this paper, it is found that the variance of RSSI value changes along with distance regu- larly by analyzing a large number of experimental data. Based on the result of analysis, we proposed the relationship function of the variance of RSSI and distance, and established the log-normal shadowing model with dynamic variance (LNSM-DV). At the same time, the method of least squares(LS) was selected to es- timate the coefficients in that model, thus LNSM-DV might be adjusted dynamically according to the change of environment and be self-adaptable. The experimental results show that LNSM-DV can further reduce er- ror, and have strong self-adaptability to various environments compared with the LNSM.展开更多
For the solutions of random variations of metal jet breakup and difficulties in controlling and predicting the process parameters （e.g. jet length） in micro droplet deposition manufacturing technique, experimental m...For the solutions of random variations of metal jet breakup and difficulties in controlling and predicting the process parameters （e.g. jet length） in micro droplet deposition manufacturing technique, experimental methods combining with theoretical analyses have been developed. The jet formation, jet length and their dominant factors （oxygen concentration and disturbance frequency, etc.） are discussed. The statistical law of jet length is found that the probability density function （PDF） of jet length is a log-normal distribution. The results show that the formation and size accuracy of metal jet breakup are improved by adjusting the gas pressure and optimizing the disturbance frequency. Under this circumstance, the jet length and morphological deviation can be minimized, which provides a stable droplet stream for the subsequent manufacturing process.展开更多
A composite random variable is a product (or sum of products) of statistically distributed quantities. Such a variable can represent the solution to a multi-factor quantitative problem submitted to a large, diverse, i...A composite random variable is a product (or sum of products) of statistically distributed quantities. Such a variable can represent the solution to a multi-factor quantitative problem submitted to a large, diverse, independent, anonymous group of non-expert respondents (the “crowd”). The objective of this research is to examine the statistical distribution of solutions from a large crowd to a quantitative problem involving image analysis and object counting. Theoretical analysis by the author, covering a range of conditions and types of factor variables, predicts that composite random variables are distributed log-normally to an excellent approximation. If the factors in a problem are themselves distributed log-normally, then their product is rigorously log-normal. A crowdsourcing experiment devised by the author and implemented with the assistance of a BBC (British Broadcasting Corporation) television show, yielded a sample of approximately 2000 responses consistent with a log-normal distribution. The sample mean was within ~12% of the true count. However, a Monte Carlo simulation (MCS) of the experiment, employing either normal or log-normal random variables as factors to model the processes by which a crowd of 1 million might arrive at their estimates, resulted in a visually perfect log-normal distribution with a mean response within ~5% of the true count. The results of this research suggest that a well-modeled MCS, by simulating a sample of responses from a large, rational, and incentivized crowd, can provide a more accurate solution to a quantitative problem than might be attainable by direct sampling of a smaller crowd or an uninformed crowd, irrespective of size, that guesses randomly.展开更多
基金supported by the Spanish Ministerio de Ciencia e Innovaciòn(PID 2020-112773 GB-I00)by Gobierno de Aragòn(ADETRE Reference GroupS39_20R).
文摘We estimate the distribution of COVID-19 mortality(measured as daily deaths)from the start of the pandemic until July 31st,2022,for six European countries and the USA.We use the Pareto,the stretched exponential,the log-normal and the log-logistic distributions as well as mixtures of the log-normal and log-logistic distributions.The main results are that the Pareto does not describe well the data and that mixture distributions tend to offer a very good fit to the data.We also compute Value-at-Risk measures as well as mortality probabilities with our estimates.We also discuss the implications of our results and findings from the point of view of public health planning and modelling.
文摘In this paper, a class of morphisms which have a kind of singularity weaker than normal crossing is considered. We construct the obstruction such that the so-called semi-stable log structures exists if and only if the obstruction vanishes. In the case of no power, if the obstruction vanishes, then the semi-stable log structure is unique up to a unique isomorphism. So we obtain a kind of canonical structure on this family of morphisms.
基金The NSF(11271155) of ChinaResearch Fund(20070183023) for the Doctoral Program of Higher Education
文摘In this paper, we propose a log-normal linear model whose errors are first-order correlated, and suggest a two-stage method for the efficient estimation of the conditional mean of the response variable at the original scale. We obtain two estimators which minimize the asymptotic mean squared error （MM） and the asymptotic bias （MB）, respectively. Both the estimators are very easy to implement, and simulation studies show that they are perform better.
文摘The relationship between RSSI (Received Signal Strength Indication) values and distance is the foundation and the key of ranging and positioning technologies in wireless sensor networks. Log-normal shadowing model (LNSM), as a more general signal propagation model, can better describe the relationship between the RSSI value and distance, but the parameter of variance in LNSM is depended on experiences without self-adaptability. In this paper, it is found that the variance of RSSI value changes along with distance regu- larly by analyzing a large number of experimental data. Based on the result of analysis, we proposed the relationship function of the variance of RSSI and distance, and established the log-normal shadowing model with dynamic variance (LNSM-DV). At the same time, the method of least squares(LS) was selected to es- timate the coefficients in that model, thus LNSM-DV might be adjusted dynamically according to the change of environment and be self-adaptable. The experimental results show that LNSM-DV can further reduce er- ror, and have strong self-adaptability to various environments compared with the LNSM.
基金National High-tech Research and Development Program of China (2008AA03A238)Fund for the Doctoral Program of Higher Education of China (20070699076)Foundation for the Author of National Excellent Doctoral Dissertation of China (2007B3)
文摘For the solutions of random variations of metal jet breakup and difficulties in controlling and predicting the process parameters （e.g. jet length） in micro droplet deposition manufacturing technique, experimental methods combining with theoretical analyses have been developed. The jet formation, jet length and their dominant factors （oxygen concentration and disturbance frequency, etc.） are discussed. The statistical law of jet length is found that the probability density function （PDF） of jet length is a log-normal distribution. The results show that the formation and size accuracy of metal jet breakup are improved by adjusting the gas pressure and optimizing the disturbance frequency. Under this circumstance, the jet length and morphological deviation can be minimized, which provides a stable droplet stream for the subsequent manufacturing process.
文摘A composite random variable is a product (or sum of products) of statistically distributed quantities. Such a variable can represent the solution to a multi-factor quantitative problem submitted to a large, diverse, independent, anonymous group of non-expert respondents (the “crowd”). The objective of this research is to examine the statistical distribution of solutions from a large crowd to a quantitative problem involving image analysis and object counting. Theoretical analysis by the author, covering a range of conditions and types of factor variables, predicts that composite random variables are distributed log-normally to an excellent approximation. If the factors in a problem are themselves distributed log-normally, then their product is rigorously log-normal. A crowdsourcing experiment devised by the author and implemented with the assistance of a BBC (British Broadcasting Corporation) television show, yielded a sample of approximately 2000 responses consistent with a log-normal distribution. The sample mean was within ~12% of the true count. However, a Monte Carlo simulation (MCS) of the experiment, employing either normal or log-normal random variables as factors to model the processes by which a crowd of 1 million might arrive at their estimates, resulted in a visually perfect log-normal distribution with a mean response within ~5% of the true count. The results of this research suggest that a well-modeled MCS, by simulating a sample of responses from a large, rational, and incentivized crowd, can provide a more accurate solution to a quantitative problem than might be attainable by direct sampling of a smaller crowd or an uninformed crowd, irrespective of size, that guesses randomly.
