A drought is when reduced rainfall leads to a water crisis,impacting daily life.Over recent decades,droughts have affected various regions,including South Sulawesi,Indonesia.This study aims to map the probability of m...A drought is when reduced rainfall leads to a water crisis,impacting daily life.Over recent decades,droughts have affected various regions,including South Sulawesi,Indonesia.This study aims to map the probability of meteo-rological drought months using the 1-month Standardized Precipitation Index(SPI)in South Sulawesi.Based on SPI,meteorological drought characteristics are inversely proportional to drought event intensity,which can be modeled using a Non-Homogeneous Poisson Process,specifically the Power Law Process.The estimation method employs Maximum Likelihood Estimation(MLE),where drought event intensities are treated as random variables over a set time interval.Future drought months are estimated using the cumulative Power Law Process function,with theβandγparameters more significant than 0.The probability of drought months is determined using the Non-Homogeneous Poisson Process,which models event occurrence over time,considering varying intensities.The results indicate that,of the 24 districts/cities in South Sulawesi,14 experienced meteorological drought based on the SPI and Power Law Process model.The estimated number of months of drought occurrence in the next 12 months is one month of drought with an occurrence probability value of 0.37 occurring in November in the Selayar,Bulukumba,Bantaeng,Jeneponto,Takalar and Gowa areas,in October in the Sinjai,Barru,Bone,Soppeng,Pinrang and Pare-pare areas,as well as in December in the Maros and Makassar areas.展开更多
Due to the simplicity and flexibility of the power law process,it is widely used to model the failures of repairable systems.Although statistical inference on the parameters of the power law process has been well deve...Due to the simplicity and flexibility of the power law process,it is widely used to model the failures of repairable systems.Although statistical inference on the parameters of the power law process has been well developed,numerous studies largely depend on complete failure data.A few methods on incomplete data are reported to process such data,but they are limited to their specific cases,especially to that where missing data occur at the early stage of the failures.No framework to handle generic scenarios is available.To overcome this problem,from the point of view of order statistics,the statistical inference of the power law process with incomplete data is established in this paper.The theoretical derivation is carried out and the case studies demonstrate and verify the proposed method.Order statistics offer an alternative to the statistical inference of the power law process with incomplete data as they can reformulate current studies on the left censored failure data and interval censored data in a unified framework.The results show that the proposed method has more flexibility and more applicability.展开更多
A fault processing policy was proposed for the circumstance under which all the dual-redundant closed-loop feedback control sensors went wrong.This policy was based on dual-redundant control law and may maintain the p...A fault processing policy was proposed for the circumstance under which all the dual-redundant closed-loop feedback control sensors went wrong.This policy was based on dual-redundant control law and may maintain the performance of turbofan engines.When pair of controlling sensors went wrong and the primary control law was unable to implement,control system performs the backup control law instead of the primary one so that the fault sensors were isolated from the closed control loop.This fault processing policy may not only avoid increasing engine weight and cost with the additional sensors hardware,but also avoid the error of analytical sensor signal.It can improve the engine mission reliability and control quality.展开更多
A new approach for studying the time-evolution law of a chaotic light field in a damping-gaining coexisting process is presented. The new differential equation for determining the parameter of the density operator p（...A new approach for studying the time-evolution law of a chaotic light field in a damping-gaining coexisting process is presented. The new differential equation for determining the parameter of the density operator p（t） is derived and the solution of f for the damping and gaining processes are studied separately. Our approach is direct and the result is concise since it is not necessary for us to know the Kraus operators in advance.展开更多
Reliability analysis is the key to evaluate software’s quality. Since the early 1970s, the Power Law Process, among others, has been used to assess the rate of change of software reliability as time-varying function ...Reliability analysis is the key to evaluate software’s quality. Since the early 1970s, the Power Law Process, among others, has been used to assess the rate of change of software reliability as time-varying function by using its intensity function. The Bayesian analysis applicability to the Power Law Process is justified using real software failure times. The choice of a loss function is an important entity of the Bayesian settings. The analytical estimate of likelihood-based Bayesian reliability estimates of the Power Law Process under the squared error and Higgins-Tsokos loss functions were obtained for different prior knowledge of its key parameter. As a result of a simulation analysis and using real data, the Bayesian reliability estimate under the Higgins-Tsokos loss function not only is robust as the Bayesian reliability estimate under the squared error loss function but also performed better, where both are superior to the maximum likelihood reliability estimate. A sensitivity analysis resulted in the Bayesian estimate of the reliability function being sensitive to the prior, whether parametric or non-parametric, and to the loss function. An interactive user interface application was additionally developed using Wolfram language to compute and visualize the Bayesian and maximum likelihood estimates of the intensity and reliability functions of the Power Law Process for a given data.展开更多
We give an extension result of Watanabe’s characterization for 2-dimensional Poisson processes. By using this result, the equivalence of uniqueness in law and joint uniqueness in law is proved for one-dimensional sto...We give an extension result of Watanabe’s characterization for 2-dimensional Poisson processes. By using this result, the equivalence of uniqueness in law and joint uniqueness in law is proved for one-dimensional stochastic differential equations driven by Poisson processes. After that, we give a simplified Engelbert theorem for the stochastic differential equations of this type.展开更多
Let {εt; t ∈ Z^＋} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2＋1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^＋} is a sequence of real numbers s...Let {εt; t ∈ Z^＋} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2＋1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^＋} is a sequence of real numbers satisfying ∑j=0^∞｜aj｜〈∞.Define a linear process Xt=∑j=0^∞ ajεt-j,t≥1,and Sn=∑t=1^n Xt,n≥1.Assume that E｜ε1｜^2＋δ′〈 for some δ′〉0 and μ（n）=O（n^-ρ） for some ρ〉0.This paper achieves a general law of precise asymptotics for {Sn}.展开更多
Let X1 XN be independent, classical Levy processes on R^d with Levy exponents ψ1,…, ψN, respectively. The corresponding additive Levy process is defined as the following N-parameter random field on R^d, X（t） △=...Let X1 XN be independent, classical Levy processes on R^d with Levy exponents ψ1,…, ψN, respectively. The corresponding additive Levy process is defined as the following N-parameter random field on R^d, X（t） △= X1（t1） ＋ ... ＋ XN（tN）, At∈N. Under mild regularity conditions on the ψi＇s, we derive estimate for the local and uniform moduli of continuity of local times of X = {X（t）; t ∈R^N}.展开更多
Let be a Gaussian process with stationary increments . Let be a nondecreasing function of t with . This paper aims to study the almost sure behaviour of where with and is an increasing sequence diverging to .
Internal solitary waves have been found to disintegrate into a series of solitons over variablebathymetry, with important applications for offshore engineering. Considering realisticbackground stratification in the So...Internal solitary waves have been found to disintegrate into a series of solitons over variablebathymetry, with important applications for offshore engineering. Considering realisticbackground stratification in the South China Sea, internal solitary waves propagating over a stepare studied here. By assuming disintegrated solitons propagate independently, a theoreticalmodel, namely a triangular temporal-distribution law based on the Korteweg–de Vries theory, isproposed to describe the fission process of internal solitary waves undergoing disintegration. Aparameter is then introduced to quantify the accuracy of the theoretical model. The resultsindicate that the triangular law predicts the fission process better for a longer travelling distanceand a larger amplitude of internal solitary waves.展开更多
Let {Xt,t ≥ 1} be a moving average process defined by Xt = ∑^∞ k=0 αkξt-k, where {αk,k ≥ 0} is a sequence of real numbers and {ξt,-∞ 〈 t 〈 ∞} is a doubly infinite sequence of strictly stationary dependen...Let {Xt,t ≥ 1} be a moving average process defined by Xt = ∑^∞ k=0 αkξt-k, where {αk,k ≥ 0} is a sequence of real numbers and {ξt,-∞ 〈 t 〈 ∞} is a doubly infinite sequence of strictly stationary dependent random variables. Under the conditions of {αk, k ≥ 0} which entail that {Xt, t ≥ 1} is either a long memory process or a linear process, the strong approximation of {Xt, t ≥ 1} to a Gaussian process is studied. Finally, the results are applied to obtain the strong approximation of a long memory process to a fractional Brownian motion and the laws of the iterated logarithm for moving average processes.展开更多
基金funded by Hasanuddin University,grant number 00309/UN4.22/PT.01.03/2024.
文摘A drought is when reduced rainfall leads to a water crisis,impacting daily life.Over recent decades,droughts have affected various regions,including South Sulawesi,Indonesia.This study aims to map the probability of meteo-rological drought months using the 1-month Standardized Precipitation Index(SPI)in South Sulawesi.Based on SPI,meteorological drought characteristics are inversely proportional to drought event intensity,which can be modeled using a Non-Homogeneous Poisson Process,specifically the Power Law Process.The estimation method employs Maximum Likelihood Estimation(MLE),where drought event intensities are treated as random variables over a set time interval.Future drought months are estimated using the cumulative Power Law Process function,with theβandγparameters more significant than 0.The probability of drought months is determined using the Non-Homogeneous Poisson Process,which models event occurrence over time,considering varying intensities.The results indicate that,of the 24 districts/cities in South Sulawesi,14 experienced meteorological drought based on the SPI and Power Law Process model.The estimated number of months of drought occurrence in the next 12 months is one month of drought with an occurrence probability value of 0.37 occurring in November in the Selayar,Bulukumba,Bantaeng,Jeneponto,Takalar and Gowa areas,in October in the Sinjai,Barru,Bone,Soppeng,Pinrang and Pare-pare areas,as well as in December in the Maros and Makassar areas.
基金supported by the National Natural Science Foundation of China(51775090)。
文摘Due to the simplicity and flexibility of the power law process,it is widely used to model the failures of repairable systems.Although statistical inference on the parameters of the power law process has been well developed,numerous studies largely depend on complete failure data.A few methods on incomplete data are reported to process such data,but they are limited to their specific cases,especially to that where missing data occur at the early stage of the failures.No framework to handle generic scenarios is available.To overcome this problem,from the point of view of order statistics,the statistical inference of the power law process with incomplete data is established in this paper.The theoretical derivation is carried out and the case studies demonstrate and verify the proposed method.Order statistics offer an alternative to the statistical inference of the power law process with incomplete data as they can reformulate current studies on the left censored failure data and interval censored data in a unified framework.The results show that the proposed method has more flexibility and more applicability.
文摘A fault processing policy was proposed for the circumstance under which all the dual-redundant closed-loop feedback control sensors went wrong.This policy was based on dual-redundant control law and may maintain the performance of turbofan engines.When pair of controlling sensors went wrong and the primary control law was unable to implement,control system performs the backup control law instead of the primary one so that the fault sensors were isolated from the closed control loop.This fault processing policy may not only avoid increasing engine weight and cost with the additional sensors hardware,but also avoid the error of analytical sensor signal.It can improve the engine mission reliability and control quality.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61141007,11047133,and 11175113)the Natural Science Foundation of Jiangxi Province of China (Grant Nos. 2010GQS0080 and 2010GQW0027)+1 种基金the Research Foundation of the Education Department of Jiangxi Province of China (Grant No. GJJ11339)the Sponsored Program for Cultivating Youths of Outstanding Ability in Jiangxi Normal University
文摘A new approach for studying the time-evolution law of a chaotic light field in a damping-gaining coexisting process is presented. The new differential equation for determining the parameter of the density operator p（t） is derived and the solution of f for the damping and gaining processes are studied separately. Our approach is direct and the result is concise since it is not necessary for us to know the Kraus operators in advance.
文摘Reliability analysis is the key to evaluate software’s quality. Since the early 1970s, the Power Law Process, among others, has been used to assess the rate of change of software reliability as time-varying function by using its intensity function. The Bayesian analysis applicability to the Power Law Process is justified using real software failure times. The choice of a loss function is an important entity of the Bayesian settings. The analytical estimate of likelihood-based Bayesian reliability estimates of the Power Law Process under the squared error and Higgins-Tsokos loss functions were obtained for different prior knowledge of its key parameter. As a result of a simulation analysis and using real data, the Bayesian reliability estimate under the Higgins-Tsokos loss function not only is robust as the Bayesian reliability estimate under the squared error loss function but also performed better, where both are superior to the maximum likelihood reliability estimate. A sensitivity analysis resulted in the Bayesian estimate of the reliability function being sensitive to the prior, whether parametric or non-parametric, and to the loss function. An interactive user interface application was additionally developed using Wolfram language to compute and visualize the Bayesian and maximum likelihood estimates of the intensity and reliability functions of the Power Law Process for a given data.
文摘We give an extension result of Watanabe’s characterization for 2-dimensional Poisson processes. By using this result, the equivalence of uniqueness in law and joint uniqueness in law is proved for one-dimensional stochastic differential equations driven by Poisson processes. After that, we give a simplified Engelbert theorem for the stochastic differential equations of this type.
基金National Natural Science Foundation of China(10571073).
文摘Let {εt; t ∈ Z^＋} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2＋1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^＋} is a sequence of real numbers satisfying ∑j=0^∞｜aj｜〈∞.Define a linear process Xt=∑j=0^∞ ajεt-j,t≥1,and Sn=∑t=1^n Xt,n≥1.Assume that E｜ε1｜^2＋δ′〈 for some δ′〉0 and μ（n）=O（n^-ρ） for some ρ〉0.This paper achieves a general law of precise asymptotics for {Sn}.
文摘Let X1 XN be independent, classical Levy processes on R^d with Levy exponents ψ1,…, ψN, respectively. The corresponding additive Levy process is defined as the following N-parameter random field on R^d, X（t） △= X1（t1） ＋ ... ＋ XN（tN）, At∈N. Under mild regularity conditions on the ψi＇s, we derive estimate for the local and uniform moduli of continuity of local times of X = {X（t）; t ∈R^N}.
文摘Let be a Gaussian process with stationary increments . Let be a nondecreasing function of t with . This paper aims to study the almost sure behaviour of where with and is an increasing sequence diverging to .
基金supported by the National Natural Science Foundation of China (11572332 and 11602274)the National Key R&D Program of China (2017YFC1404202)the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB22040203)
文摘Internal solitary waves have been found to disintegrate into a series of solitons over variablebathymetry, with important applications for offshore engineering. Considering realisticbackground stratification in the South China Sea, internal solitary waves propagating over a stepare studied here. By assuming disintegrated solitons propagate independently, a theoreticalmodel, namely a triangular temporal-distribution law based on the Korteweg–de Vries theory, isproposed to describe the fission process of internal solitary waves undergoing disintegration. Aparameter is then introduced to quantify the accuracy of the theoretical model. The resultsindicate that the triangular law predicts the fission process better for a longer travelling distanceand a larger amplitude of internal solitary waves.
文摘Let {Xt,t ≥ 1} be a moving average process defined by Xt = ∑^∞ k=0 αkξt-k, where {αk,k ≥ 0} is a sequence of real numbers and {ξt,-∞ 〈 t 〈 ∞} is a doubly infinite sequence of strictly stationary dependent random variables. Under the conditions of {αk, k ≥ 0} which entail that {Xt, t ≥ 1} is either a long memory process or a linear process, the strong approximation of {Xt, t ≥ 1} to a Gaussian process is studied. Finally, the results are applied to obtain the strong approximation of a long memory process to a fractional Brownian motion and the laws of the iterated logarithm for moving average processes.
