IN THIS PAPER, A NEW FAMILY OF CONTINUOUS DISTRIBUTIONS WITH POSITIVE SUPPORT IS INTRODUCED. THIS FAMILY IS GENERATED BY A TRUNCATION OF THE FAMILY OF UNIVARIATE SYMMETRICAL DISTRIBUTIONS. IN THIS NEW FAMILY OF DISTRIBUTIONS, GENERAL PROPERTIES, SUCH AS MOMENTS, ASYMMETRY AND KURTOSIS COEFFICIENTS, ARE DERIVED. PARTICULAR CASES OF INTEREST BASED ON THE NORMAL, LOGISTIC, LAPLACE AND CAUCHY MODELS ARE DISCUSSED IN DEPTH. THE ESTIMATION OF PARAMETERS IS CARRIED OUT BY APPLYING MOMENTS AND MAXIMUM LIKELIHOOD METHODS. ALSO, A SIMULATION STUDY WAS CONDUCTED TO ILLUSTRATE THE GOOD PERFORMANCE OF ESTIMATORS. AN APPLICATION TO THE SURVIVAL TIMES (IN DAYS) OF GUINEA PIGS DATASET IS INCLUDED, WHERE THE SPECIAL CASES OF DISTRIBUTIONS IN THIS FAMILY ARE FITTED. THE OPTION WHICH PROVIDES THE BEST FIT IS ULTIMATELY CHOSEN. AN R PACKAGE, CALLED ?TPN?, HAS BEEN IMPLEMENTED, WHICH INCLUDES THE RELEVANT CASES OF INTEREST IN THIS FAMILY.

IN THIS PAPER, WE EXTEND THE LOMAX-RAYLEIGH DISTRIBUTION TO INCREASE ITS KURTOSIS. THE CONSTRUCTION OF THIS DISTRIBUTION IS BASED ON THE IDEA OF THE SLASH DISTRIBUTION, THAT IS, ITS REPRESENTATION IS BASED ON THE QUOTIENT OF TWO INDEPENDENT RANDOM VARIABLES, ONE BEING A RANDOM VARIABLE WITH A LOMAX-RAYLEIGH DISTRIBUTION AND THE OTHER A BETA(Q,1). BASED ON THE REPRESENTATION OF THIS FAMILY, WE STUDY ITS BASIC PROPERTIES, SUCH AS MOMENTS, COEFFICIENTS OF SKEWNESS, AND KURTOSIS. WE PERFORM STATISTICAL INFERENCE USING THE METHODS OF MOMENTS AND MAXIMUM LIKELIHOOD. TO ILLUSTRATE THIS METHODOLOGY, WE APPLY IT TO TWO REAL DATA SETS.

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 A NEW MODEL WITH POSITIVE SUPPORT. THIS MODEL IS AN EXTENSION OF THE TRUNCATED GUMBEL DISTRIBUTION, WHERE A SHAPE PARAMETER IS INCORPORATED THAT PROVIDES GREATER FLEXIBILITY TO THE NEW MODEL. THE MODEL IS PARAMETERIZED IN TERMS OF THE P-TH QUANTILE OF THE DISTRIBUTION TO PERFORM QUANTILE REGRESSION IN THIS MODEL. AN EXTENSIVE SIMULATION STUDY DEMONSTRATES THE GOOD PERFORMANCE OF THE MAXIMUM LIKELIHOOD ESTIMATORS IN FINITE SAMPLES. FINALLY, TWO APPLICATIONS TO REAL DATASETS RELATED TO THE LEVEL OF BETA-CAROTENE AND BODY MASS INDEX ARE PRESENTED.

WE INTRODUCE A NEW MODELLING FOR LONG-TERM SURVIVAL MODELS, ASSUMING THAT THE NUMBER OF COMPETING CAUSES FOLLOWS A MIXTURE OF POISSON AND THE BIRNBAUM-SAUNDERS DISTRIBUTION. IN THIS CONTEXT, WE PRESENT SOME STATISTICAL PROPERTIES OF OUR MODEL AND DEMONSTRATE THAT THE PROMOTION TIME MODEL EMERGES AS A LIMITING CASE. WE DELVE INTO DETAILED DISCUSSIONS OF SPECIFIC MODELS WITHIN THIS CLASS. NOTABLY, WE EXAMINE THE EXPECTED NUMBER OF COMPETING CAUSES, WHICH DEPENDS ON COVARIATES. THIS ALLOWS FOR DIRECT MODELING OF THE CURE RATE AS A FUNCTION OF COVARIATES.WE PRESENT AN EXPECTATION-MAXIMIZATION (EM) ALGORITHM FOR PARAMETER ESTIMATION, TO DISCUSS THE ESTIMATION VIA MAXIMUM LIKELIHOOD (ML) AND PROVIDE INSIGHTS INTO PARAMETER INFERENCE FOR THIS MODEL. ADDITIONALLY, WE OUTLINE SUFFICIENT CONDITIONS FOR ENSURING THE CONSISTENCY AND ASYMPTOTIC NORMAL DISTRIBUTION OF ML ESTIMATORS. TO EVALUATE THE PERFORMANCE OF OUR ESTIMATION METHOD, WE CONDUCT A MONTE CARLO SIMULATION TO PROVIDE ASYMPTOTIC PROPERTIES AND A POWER STUDY OF LR TEST BY CONTRASTING OUR METHODOLOGY AGAINST THE PROMOTION TIME MODEL. TO DEMONSTRATE THE PRACTICAL APPLICABILITY OF OUR MODEL, WE APPLY IT TO A REAL MEDICAL DATASET FROM A POPULATION-BASED STUDY OF INCIDENCE OF BREAST CANCER IN SÃO PAULO, BRAZIL. OUR RESULTS ILLUSTRATE THAT THE PROPOSED MODEL CAN OUTPERFORM TRADITIONAL APPROACHES IN TERMS OF MODEL FITTING, HIGHLIGHTING ITS POTENTIAL UTILITY IN REAL-WORLD SCENARIOS.

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.

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.

WE PRESENT A NOVEL FRAILTY MODEL FOR MODELING CLUSTERED SURVIVAL DATA. IN PARTICULAR, WE CONSIDER THE BIRNBAUM-SAUNDERS (BS) DISTRIBUTION FOR THE FRAILTY TERMS WITH A NEW DIRECTLY PARAMETERIZED ON THE VARIANCE OF THE FRAILTY DISTRIBUTION. THIS ALLOWS, AMONG OTHER THINGS, COMPARE THE ESTIMATED FRAILTY TERMS AMONG TRADITIONAL MODELS, SUCH AS THE GAMMA FRAILTY MODEL. SOME MATHEMATICAL PROPERTIES OF THE NEW MODEL ARE STUDIED INCLUDING THE CONDITIONAL DISTRIBUTION OF FRAILTIES AMONG THE SURVIVORS, THE FRAILTY OF INDIVIDUALS DYING AT TIME T, AND THE KENDALL

CURE RATE MODELS HAVE BEEN WIDELY STUDIED TO ANALYZE TIME-TO-EVENT DATA WITH A CURED FRACTION OF PATIENTS. IN THIS TYPE OF MODEL, THE NUMBER OF CONCURRENT CAUSES IS ASSUMED TO BE A RANDOM VARIABLE. HOWEVER, IN PRACTICE, IT IS NATURAL TO ADMIT THAT THE DISTRIBUTION OF THE NUMBER OF COMPETING CAUSES IS DIFFERENT FROM INDIVIDUAL TO INDIVIDUAL. OUR PROPOSAL IS TO ASSUME THAT THE NUMBER OF COMPETING CAUSES BELONGS TO A CLASS OF A FINITE MIXTURE OF COMPETING CAUSES DISTRIBUTIONS. WE ASSUME THE NUMBER OF MALIGNANT CELLS FOLLOW A MIXTURE OF TWO POWER SERIES DISTRIBUTIONS AND SUPPOSE THAT THE TIME TO THE EVENT OF INTEREST FOLLOWS A WEIBULL DISTRIBUTION. WE CONSIDER THE PROPORTION OF THE CURED NUMBER OF COMPETING CAUSES DEPENDING ON COVARIATES, ALLOWING DIRECT MODELING OF THE CURE RATE. THE PROPOSED MODEL INCLUDES SEVERAL WELL-KNOWN MODELS AS SPECIAL CASES AND DEFINES MANY NEW SPECIAL MODELS. AN EXPECTATION-MAXIMIZATION ALGORITHM IS PROPOSED FOR PARAMETER ESTIMATION, WHERE THE EXPECTATION STEP INVOLVES THE COMPUTATION OF THE EXPECTED NUMBER OF CONCURRENT CAUSES FOR EACH INDIVIDUAL. A MONTE CARLO SIMULATION IS PERFORMED TO ASSESS THE BEHAVIOR OF THE ESTIMATION METHOD. IN ORDER TO SHOW THE POTENTIAL FOR THE PRACTICE OF OUR MODEL, WE APPLY IT TO THE REAL MEDICAL DATA SET FROM A POPULATION-BASED STUDY OF INCIDENT CASES OF CUTANEOUS MELANOMA DIAGNOSED IN THE STATE OF SÃO PAULO, BRAZIL, ILLUSTRATING THAT THE MODEL PROPOSED CAN OUTPERFORM TRADITIONAL MODELS IN TERMS OF MODEL FITTING.

THE LITERATURE HAS EXAMINED INDIVIDUAL PREDICTORS OF ATTITUDES TOWARD IMMIGRANTS, CONTROLLED BY SUPRA-INDIVIDUAL VARIABLES, ESPECIALLY IN EUROPEAN AND NORTH AMERICAN COUNTRIES. NEVERTHELESS, THIS ANALYSIS HAS NOT BEEN MADE USING SOUTH-SOUTH MIGRATION COMMUNITIES. THUS, THIS STUDY ANALYZED THE INDIVIDUAL PREDICTORS OF THE ATTITUDES TOWARD IMMIGRANTS FROM PER & UACUTE; AND VENEZUELA IN A CHILEAN SAMPLE, CONTROLLING SUPRA-INDIVIDUAL VARIABLES. WE USED AVAILABLE DATA (N TOTAL = 956, COMPOSED OF 599 AND 357 FOR PERUVIANS AND VENEZUELANS, RESPECTIVELY), CONSIDERING SEVEN PREDICTORS AND THREE TYPES OF INTERGROUP ATTITUDES. THE MAIN RESULTS INDICATED THAT CONTACT QUALITY, SIMILARITY AND SOCIAL DOMINANCE ORIENTATION WERE RELATED TO ALMOST ALL TYPES OF ATTITUDES (SYMBOLIC THREAT, REALISTIC THREAT AND LIKING) TOWARD BOTH IMMIGRANT POPULATIONS, EXCEPT THAT SIMILARITY AND DOMINANCE ORIENTATION WERE NOT ASSOCIATED WITH REALISTIC THREATS AND LIKING TOWARD VENEZUELANS, RESPECTIVELY. THE REST OF THE PREDICTORS, CONTACT QUANTITY, GENERALIZED TRUST, POLITICAL ORIENTATION, AND RIGHT-WING AUTHORITARIANISM EXPLAINED THREE OR FEWER TYPES OF ATTITUDES TOWARD BOTH IMMIGRANT COMMUNITIES. WE SPECULATED ABOUT THE REASONS WHY CONTACT QUALITY, SIMILARITY AND SOCIAL DOMINANCE ORIENTATION WERE ASSOCIATED WITH MORE TYPES OF ATTITUDES THAN THE REST OF THE PREDICTORS, AND THE PRESENT MODEL

THE LAST HYDROMETEOROLOGICAL EXTREME EVENT THAT CAUSED LARGE FLOODS IN THE SOUTHERN ATACAMA DESERT IN MARCH 2015 RAISED CONCERN ABOUT HOW LITTLE WAS KNOWN ABOUT THE FLUVIAL DYNAMIC OF THESE ARID BASINS. UNDERSTANDING THE RESPONSE OF INTERMITTENT AND EPHEMERAL RIVERS IN DRYLANDS TO THE PRESENT CONTEXT OF GLOBAL CHANGE IS CRITICAL TO PRESERVE THE ECOLOGICAL AND HUMAN SYSTEMS THEY SUPPORT, TO SUSTAINABLY MANAGE THEIR SCARCE WATER RESOURCES AND TO DEVELOP FLOOD RISK MANAGEMENT PLANS. WE HAVE STUDIED THE INSTRUMENTAL AND HISTORICAL RECORD AND EXPLORED THE POTENTIAL OF THE COPIAP

IN THIS PAPER, WE DEVELOP A FULLY PARAMETRIC QUANTILE REGRESSION MODEL BASED ON THE GENERALISED THREE-PARAMETER BETA (GB3) DISTRIBUTION. BETA REGRESSION MODELS ARE PRIMARILY USED TO MODEL RATES AND PROPORTIONS. HOWEVER, THESE MODELS ARE USUALLY SPECIFIED IN TERMS OF A CONDITIONAL MEAN. THEREFORE, THEY MAY BE INADEQUATE IF THE OBSERVED RESPONSE VARIABLE FOLLOWS AN ASYMMETRICAL DIS- TRIBUTION. IN ADDITION, BETA REGRESSION MODELS DO NOT CONSIDER THE EFFECT OF THE COVARIATES ACROSS THE SPECTRUM OF THE DEPENDENT VARIABLE, WHICH IS POSSIBLE THROUGH THE CONDITIONAL QUANTILE APPROACH. IN ORDER TO INTRODUCE THE PROPOSED GB3 REGRESSION MODEL, WE FIRST REPARAMETERISE THE GB3 DISTRIBUTION BY INSERTING A QUANTILE PARAMETER, AND THEN WE DEVELOP THE NEW PROPOSED QUANTILE MODEL. WE ALSO PROPOSE A SIMPLE INTERPRETATION OF THE PREDICTOR?RESPONSE RELATIONSHIP IN TERMS OF PERCENTAGE INCREASES/DECREASES OF THE QUANTILE. A MONTE CARLO STUDY IS CARRIED OUT FOR EVALUATING THE PERFORMANCE OF THE MAXIMUM LIKELIHOOD ESTIMATES AND THE CHOICE OF THE LINK FUNCTIONS. FINALLY, A REAL COVID-19 DATASET FROM CHILE IS ANALYSED AND DISCUSSED TO ILLUSTRATE THE PROPOSED APPROACH.

IN THIS PAPER, WE INTRODUCE A NEW PARAMETERIZATION FOR THE SCALE MIXTURE OF THE RAYLEIGH DISTRIBUTION, WHICH USES A MEAN LINEAR REGRESSION MODEL INDEXED BY MEAN AND PRECISION PARAMETERS TO MODEL ASYMMETRIC POSITIVE REAL DATA. TO TEST THE GOODNESS OF FIT, WE INTRODUCE TWO RESIDUALS FOR THE NEW MODEL. A MONTE CARLO SIMULATION STUDY IS PERFORMED TO EVALUATE THE PARAMETER ESTIMATION OF THE PROPOSED MODEL. WE COMPARE OUR PROPOSED MODEL WITH EXISTING ALTERNATIVES AND ILLUSTRATE ITS ADVANTAGES AND USEFULNESS USING GILGAIS DATA IN R SOFTWARE VERSION 4.2.3 WITH THE GAMLSS PACKAGE.