TO EVALUATE THE IMMUNE RESPONSE TO THE SARS-COV-2 VACCINES IN ADULTS WITH IMMUNE-MEDIATED RHEUMATIC DISEASES (IMRDS) IN COMPARISON TO HEALTHY INDIVIDUALS, OBSERVED 1-20 WEEKS FOLLOWING THE FOURTH VACCINE DOSE. ADDITIONALLY, TO EVALUATE THE IMPACT OF IMMUNOSUPPRESSIVE THERAPIES, VACCINATION SCHEDULES, THE TIME INTERVAL BETWEEN VACCINATION AND SAMPLE COLLECTION ON THE VACCINE?S IMMUNE RESPONSE. PERFORMING A COMPARISON BETWEEN THE VARIANTS, WUHAN VS OMICRON, WE NOTICED THAT THERE WERE SIGNIFICANT DIFFERENCES (P

A NOVEL CURE RATE MODEL IS INTRODUCED BY CONSIDERING, FOR THE NUMBER OF CONCURRENT CAUSES, THE MODIFIED POWER SERIES DISTRIBUTION AND, FOR THE TIME TO EVENT, THE RECENTLY PROPOSED POWER PIECEWISE EXPONENTIAL DISTRIBUTION. THIS MODEL INCLUDES A WIDE VARIETY OF CURE RATE MODELS, SUCH AS BINOMIAL, POISSON, NEGATIVE BINOMIAL, HAIGHT, BOREL, LOGARITHMIC, AND RESTRICTED GENERALIZED POISSON. SOME CHARACTERISTICS OF THE MODEL ARE EXAMINED, AND THE ESTIMATION OF PARAMETERS IS PERFORMED USING THE EXPECTATION-MAXIMIZATION ALGORITHM. A SIMULATION STUDY IS PRESENTED TO EVALUATE THE PERFORMANCE OF THE ESTIMATORS IN FINITE SAMPLES. FINALLY, AN APPLICATION IN A REAL MEDICAL DATASET FROM A POPULATION-BASED STUDY OF INCIDENT CASES OF LOBULAR CARCINOMA DIAGNOSED IN THE STATE OF SAO PAULO, BRAZIL, ILLUSTRATES THE ADVANTAGES OF THE PROPOSED MODEL COMPARED TO OTHER COMMON CURE RATE MODELS IN THE LITERATURE, PARTICULARLY REGARDING THE UNDERESTIMATION OF THE CURE RATE IN OTHER PROPOSALS AND THE IMPROVED PRECISION IN ESTIMATING THE CURE RATE OF OUR PROPOSAL.

IN THIS ARTICLE WE INTRODUCE AN EXTENSION OF THE AKASH DISTRIBUTION. WE USE THE SLASH METHODOLOGY TO MAKE THE KURTOSIS OF THE AKASH DISTRIBUTION MORE FLEXIBLE. WE STUDY THE GENERAL PROBABILITY DENSITY FUNCTION OF THIS NEW MODEL, SOME PROPERTIES, MOMENTS, SKEWNESS AND KURTOSIS COEFFICIENTS. STATISTICAL INFERENCE IS PERFORMED USING THE METHODS OF MOMENTS AND MAXIMUM LIKELIHOOD VIA THE EM ALGORITHM. A SIMULATION STUDY IS CARRIED OUT TO OBSERVE THE BEHAVIOR OF THE MAXIMUM LIKELIHOOD ESTIMATOR. AN APPLICATION TO A REAL DATA SET WITH HIGH KURTOSIS IS CONSIDERED, WHERE IT IS SHOWN THAT THE NEW DISTRIBUTION FITS BETTER THAN OTHER EXTENSIONS OF THE AKASH DISTRIBUTION.

THIS PAPER PRESENTS THE SLASH-EXPONENTIAL-FRÉCHET DISTRIBUTION, WHICH IS AN EXPANDED VERSION OF THE FRÉCHET DISTRIBUTION. THROUGH ITS STOCHASTIC REPRESENTATION, PROBABILITY DISTRIBUTION FUNCTION, MOMENTS AND OTHER RELEVANT FEATURES ARE OBTAINED. EVIDENCE SUPPORTS THAT THE UPDATED MODEL DISPLAYS A LIGHTER RIGHT TAIL THAN THE FRÉCHET MODEL AND IS MORE FLEXIBLE AS FOR SKEWNESS AND KURTOSIS. RESULTS ON MAXIMUM LIKELIHOOD ESTIMATORS ARE GIVEN. OUR PROPOSITION?S APPLICABILITY IS DEMONSTRATED THROUGH A SIMULATION STUDY AND THE EVALUATION OF TWO REAL-WORLD DATASETS.

THE WEIBULL DISTRIBUTION IS A VERSATILE PROBABILITY DISTRIBUTION WIDELY APPLIED IN MODELING THE FAILURE TIMES OF OBJECTS OR SYSTEMS. ITS BEHAVIOR IS SHAPED BY TWO ESSENTIAL PARAMETERS: THE SHAPE PARAMETER AND THE SCALE PARAMETER. BY MANIPULATING THESE PARAMETERS, THE WEIBULL DISTRIBUTION ADEPTLY CAPTURES DIVERSE FAILURE PATTERNS OBSERVED IN REAL-WORLD SCENARIOS. THIS FLEXIBILITY AND BROAD APPLICABILITY MAKE IT AN INDISPENSABLE TOOL IN RELIABILITY ANALYSIS AND SURVIVAL MODELING. THIS MANUSCRIPT EXPLORES FIVE PARAMETERIZATIONS OF THE WEIBULL DISTRIBUTION, EACH BASED ON DIFFERENT MOMENTS, LIKE MEAN, QUANTILE, AND MODE. IT METICULOUSLY CHARACTERIZES EACH PARAMETERIZATION, INTRODUCING A NOVEL ONE BASED ON THE MODEL?S MODE, ALONG WITH ITS HAZARD AND SURVIVAL FUNCTIONS, SHEDDING LIGHT ON THEIR UNIQUE PROPERTIES. ADDITIONALLY, IT DELVES INTO THE INTERPRETATION OF REGRESSION COEFFICIENTS WHEN INCORPORATING REGRESSION STRUCTURES INTO THESE PARAMETERIZATIONS. IT IS ANALYTICALLY ESTABLISHED THAT ALL FIVE PARAMETERIZATIONS DEFINE THE SAME LOG-LIKELIHOOD FUNCTION, UNDERLINING THEIR EQUIVALENCE. THROUGH MONTE CARLO SIMULATION STUDIES, THE PERFORMANCES OF THESE PARAMETERIZATIONS ARE EVALUATED IN TERMS OF PARAMETER ESTIMATIONS AND RESIDUALS. THE MODELS ARE FURTHER APPLIED TO REAL-WORLD DATA, ILLUSTRATING THEIR EFFECTIVENESS IN ANALYZING MATERIAL FATIGUE LIFE AND SURVIVAL DATA. IN SUMMARY, THIS MANUSCRIPT PROVIDES A COMPREHENSIVE EXPLORATION OF THE WEIBULL DISTRIBUTION AND ITS VARIOUS PARAMETERIZATIONS. IT OFFERS VALUABLE INSIGHTS INTO THEIR APPLICATIONS AND IMPLICATIONS IN MODELING FAILURE TIMES, WITH POTENTIAL CONTRIBUTIONS TO DIVERSE FIELDS REQUIRING RELIABILITY AND SURVIVAL ANALYSIS.

IN THIS PAPER WE STUDY SOME METHODS TO REDUCE THE BIAS FOR MAXIMUM LIKELIHOOD ESTIMATION IN THE GENERAL CLASS OF ALPHA POWER MODELS, SPECIFICALLY FOR THE SHAPE PARAMETER. WE FIND THE MODIFIED MAXIMUM LIKELIHOOD ESTIMATOR USING FIRTH'S METHOD AND WE SHOW THAT THIS ESTIMATOR IS THE UNIFORMLY MINIMUM VARIANCE UNBIASED ESTIMATOR (UMVUE) IN THIS CLASS. WE CONSIDER THREE SPECIAL CASES OF THIS CLASS, NAMELY THE EXPONENTIATED EXPONENTIAL (EE), THE POWER HALF-NORMAL AND THE POWER PIECEWISE EXPONENTIAL MODELS. WE COMPARE THE BIAS IN SIMULATION STUDIES AND FIND THAT THE MODIFIED METHOD IS DEFINITELY SUPERIOR, ESPECIALLY FOR SMALL SAMPLE SIZES, IN BOTH THE BIAS AND THE ROOT MEAN SQUARED ERROR. WE ILLUSTRATE OUR MODIFIED ESTIMATOR IN FOUR REAL DATA SET EXAMPLES, IN EACH OF WHICH THE MODIFIED ESTIMATES BETTER EXPLAIN THE VARIABILITY.

THIS ARTICLE PRESENTS AN EXTENDED DISTRIBUTION THAT BUILDS UPON THE EXPONENTIAL DISTRIBUTION. THIS EXTENSION IS BASED ON A SCALE MIXTURE BETWEEN THE EXPONENTIAL AND BETA DISTRIBUTIONS. BY UTILIZING THIS APPROACH, WE OBTAIN A DISTRIBUTION THAT OFFERS INCREASED FLEXIBILITY IN TERMS OF THE KURTOSIS COEFFICIENT. WE EXPLORE THE GENERAL DENSITY, PROPERTIES, MOMENTS, ASYMMETRY, AND KURTOSIS COEFFICIENTS OF THIS DISTRIBUTION. STATISTICAL INFERENCE IS PERFORMED USING BOTH THE MOMENTS AND MAXIMUM LIKELIHOOD METHODS. TO SHOW THE PERFORMANCE OF THIS NEW MODEL, IT IS APPLIED TO A REAL DATASET WITH ATYPICAL OBSERVATIONS. THE RESULTS INDICATE THAT THE NEW MODEL OUTPERFORMS TWO OTHER EXTENSIONS OF THE EXPONENTIAL DISTRIBUTION.

IN THIS PAPER, WE PRESENT THE UNIT-POWER HALF-NORMAL DISTRIBUTION, DERIVED FROM THE POWER HALF-NORMAL DISTRIBUTION, FOR DATA ANALYSIS IN THE OPEN UNIT INTERVAL. THE STATISTICAL PROPERTIES OF THE UNIT-POWER HALF-NORMAL MODEL ARE DESCRIBED IN DETAIL. SIMULATION STUDIES ARE CARRIED OUT TO EVALUATE THE PERFORMANCE OF THE PARAMETER ESTIMATORS. ADDITIONALLY, WE IMPLEMENT THE QUANTILE REGRESSION FOR THIS MODEL, WHICH IS APPLIED TO TWO REAL HEALTHCARE DATA SETS. OUR FINDINGS SUGGEST THAT THE UNIT POWER HALF-NORMAL DISTRIBUTION PROVIDES A ROBUST AND FLEXIBLE ALTERNATIVE FOR EXISTING MODELS FOR PROPORTION DATA.