DETECTING BIMODALITY OF A FREQUENCY DISTRIBUTION IS OF CONSIDERABLE INTEREST IN SEVERAL FIELDS. CLASSICAL INFERENTIAL METHODS FOR DETECTING BIMODALITY FOCUSED IN THIRD AND FOURTH MOMENTS THROUGH THE KURTOSIS MEASURE. NONPARAMETRIC APPROACH-BASED ASYMPTOTIC TESTS (DIPTEST) FOR COMPARING THE EMPIRICAL DISTRIBUTION FUNCTION WITH A UNIMODAL ONE ARE ALSO AVAILABLE. THE LATTER POINT DRIVES THIS PAPER, BY CONSIDERING A PARAMETRIC APPROACH USING THE BIMODAL SKEW-SYMMETRIC NORMAL DISTRIBUTION. THIS GENERAL CLASS CAPTURES BIMODALITY, ASYMMETRY AND EXCESS OF KURTOSIS IN DATA SETS. THE KULLBACK?LEIBLER DIVERGENCE IS CONSIDERED TO OBTAIN THE STATISTIC?S TEST. SOME COMPARISONS WITH DIPTEST, SIMULATIONS, AND THE STUDY OF SEA SURFACE TEMPERATURE DATA ILLUSTRATE THE USEFULNESS OF PROPOSED METHODOLOGY.

THE SOUTHERN HUMBOLDT CURRENT ECOSYSTEM IS AN IMPORTANT TOPIC AMONG RESEARCHERS WORKING ON THE DRIVERS OF PELAGIC SPECIES BIOLOGICAL INDICATORS. WHILE SEA SURFACE TEMPERATURE IS BELIEVED TO BE A MAJOR DRIVER IN ANCHOVIES (ENGRAULIS RINGENS) REPRODUCTIVE AND BODY CONDITION INDICATORS, THIS PAPER SHOWS THAT REGIONAL DRIVERS SUCH AS PACIFIC DECADAL OSCILLATION ANOMALIES ALSO INFLUENCE THESE BIOLOGICAL PROCESSES. IN ADDITION, A WARM CONDITION COULD TRIGGER INCREASED GONAD DEVELOPMENT OF ANCHOVIES AND SYNCHRONIZATION OF BODY CONDITION DYNAMICS WITH LOCAL ENVIRONMENTAL CONDITIONS STEMMING FROM SEA TURBULENCE AND EKMAN TRANSPORT. TO TEST THE STATISTICAL SIGNIFICANCE OF CAUSALITY BETWEEN TWO TIME SERIES AND DETERMINE THE DIRECTION OF CAUSALITY, THE FREQUENCY-DOMAIN GRANGER-CAUSALITY METHOD IS CONSIDERED. THEREFORE, THIS STUDY PROVIDES ADDITIONAL PREDICTIVE INFORMATION, DERIVED FROM PAST DATA ON ANCHOVY REPRODUCTIVE AND FEEDING ACTIVITIES. THE STUDY COULD BE USEFUL FOR RESEARCHERS WORKING ON RELATIONSHIPS OF ENVIRONMENTAL CONDITIONS AND PELAGIC SPECIES TO PREDICT BIOLOGICAL PROCESSES MAXIMUM AND MINIMUM PEAK MOVEMENTS AND ANCHOVY ABUNDANCE IN THE SOUTHERN HUMBOLDT CURRENT ECOSYSTEM.

IN THIS PAPER WE ADDRESSED THE PROBLEM OF BACKCASTING AND FORECASTING NON-STATIONARY TIME SERIES. GIVEN THAT TRADITIONAL BACKCASTING ARE BASED ON THE CLASSICAL CROSS-CORRELATION FUNCTION ASSUMING TWO STATIONARY TIME SERIES, ASSUMPTIONS BASED ON TWO NON-STATIONARY TIME SERIES NEED A NEW APPROACH. THUS, DETRENDED CROSS-CORRELATION ANALYSIS (DCCA) PROVIDES A FANNED ESTIMATOR FOR A CORRELATION BETWEEN TWO NON-STATIONARY TIME SERIES, PROVIDING THEN THE STATIONARY TIME SERIES. THEREFORE, WE DEVELOPED A BACKCASTER ESTIMATOR AND A PREDICTOR FOR THE OBTAINED STATIONARY TIME SERIES. THE PRACTICAL EXAMPLE OF A CHILEAN CEMENT PRODUCTION TIME SERIES (1991?2015) ILLUSTRATES OUR RESULTS.

THE UNIVARIATE GAMMA (CHI-SQUARED) SUPERSTATISTICS HAS BEEN USED IN SEVERAL APPLICATIONS BY ASSUMING INDEPENDENCE BETWEEN SYSTEMS. HOWEVER, IN SOME CASES IT SEEMS MORE REASONABLE TO CONSIDER A DEPENDENCE STRUCTURE. THIS FACT MOTIVATES THE INTRODUCTION OF A FAMILY OF BIVARIATE SUPERSTATISTICS BASED ON AN EXTENSION OF THE GAMMA DISTRIBUTION, DEFINED BY GENERALIZED HYPERGEOMETRIC FUNCTIONS. THE PARTICULAR CASES INCLUDE BOLTZMANN AND OTHER STATISTICAL WEIGHTING FACTORS IN THE LITERATURE. NUMERICAL ILLUSTRATIONS SHOW THE BEHAVIOUR OF THE PROPOSED SUPERSTATISTICS.

MIXTURE MODELS ARE IN HIGH DEMAND FOR MACHINE-LEARNING ANALYSIS DUE TO THEIR COMPUTATIONAL TRACTABILITY, AND BECAUSE THEY SERVE AS A GOOD APPROXIMATION FOR CONTINUOUS DENSITIES. PREDOMINANTLY, ENTROPY APPLICATIONS HAVE BEEN DEVELOPED IN THE CONTEXT OF A MIXTURE OF NORMAL DENSITIES. IN THIS PAPER, WE CONSIDER A NOVEL CLASS OF SKEW-NORMAL MIXTURE MODELS, WHOSE COMPONENTS CAPTURE SKEWNESS DUE TO THEIR FLEXIBILITY. WE FIND UPPER AND LOWER BOUNDS FOR SHANNON AND RÉNYI ENTROPIES FOR THIS MODEL. USING SUCH A PAIR OF BOUNDS, A CONFIDENCE INTERVAL FOR THE APPROXIMATE ENTROPY VALUE CAN BE CALCULATED. IN ADDITION, AN ASYMPTOTIC EXPRESSION FOR RÉNYI ENTROPY BY STIRLING?S APPROXIMATION IS GIVEN, AND UPPER AND LOWER BOUNDS ARE REPORTED USING MULTINOMIAL COEFFICIENTS AND SOME PROPERTIES AND INEQUALITIES OF LP METRIC SPACES. SIMULATION STUDIES ARE THEN APPLIED TO A SWORDFISH (XIPHIAS GLADIUS LINNAEUS) LENGTH DATASET.

THERE REMAINS A LACK OF HOLISTIC APPROACHES FOR ANALYZING HOW DIFFERENT DENSITY-INDEPENDENT AND DENSITY-DEPENDENT (ENDOGENOUS) MECHANISMS INTERACT TO DRIVE THE DYNAMICS OF THE SMALL PELAGIC FISH POPULATIONS OF THE SOUTHERN HUMBOLDT CURRENT ECOSYSTEM. IN THIS STUDY, WE ANALYZED THE DRIVERS OF THE SMALL PELAGIC FISHES (SPF) OFF THE COAST OF CHILE FROM THE LATE 1980S UNTIL THE EARLY 2010S. WE POSTULATED THAT CLIMATE, FISHING, AND ENDOGENOUS EFFECTS DROVE THE BIOMASS DYNAMICS OF THESE POPULATIONS. PER CAPITA GROWTH RATES (R MODELS) WERE USED TO INVESTIGATE HOW THESE FACTORS REGULATED THE DYNAMICS OF THREE ANCHOVY POPULATIONS AND ONE POPULATION OF COMMON SARDINE (CS) OFF THE CHILEAN COAST. WE FOUND THAT THE DYNAMICS OF THE ANCHOVY POPULATIONS LOCATED OFF NORTHERN CHILE WERE DRIVEN BY ENDOGENOUS COMPONENTS AND BY THE EFFECTS OF THE CLIMATE, FISHING, AND THE CLIMATE?FISHING INTERACTION. WE PROPOSED THAT DURING THE STUDY PERIOD, THE CLIMATE CONDITIONS FAVORED THE POPULATION GROWTH OF THE ANCHOVIES IN THE NORTH; HOWEVER, FISHING HAD A NEGATIVE EFFECT ON ANCHOVY BIOMASS, WHICH WAS FACILITATED BY THE CLIMATE. THE DYNAMICS OF THE SPF OFF CENTRAL-SOUTHERN CHILE SHOWED WEAKER ENDOGENOUS EFFECTS. INDEED, THE ANCHOVY POPULATION DISPLAYED THE LOWEST DENSITY-DEPENDENT EFFECT, AND FISHING PLAYED THE MOST SIGNIFICANT ROLE. THE ENDOGENOUS EFFECT ON THE CS WAS SLIGHTLY HIGHER IN COMPARISON TO THAT ON THE ANCHOVY; HOWEVER, CLIMATE [SEA SURFACE TEMPERATURE (SST)] SEEMED TO BE THE MAIN DRIVER OF THE FLOURISHMENT IN THE CS BIOMASS FOLLOWING 2006, WHICH SUPPORTED THE PREVIOUS HYPOTHESIS REGARDING THE EFFECT OF CLIMATE ON THE SPECIES. WE DISCUSSED THAT THE R MODELS APPROACH COULD BE USED TO PROVIDE A HOLISTIC UNDERSTANDING OF THE DRIVERS OF THE BIOMASS DYNAMICS OF THESE POPULATIONS. THE APPROACH PROVIDED A FRAMEWORK FOR INTEGRATING CLIMATE VARIABILITY IN THE POPULATION DYNAMICS OF THESE SPECIES AND MOVING TOWARD AN ECOSYSTEM APPROACH TO FISHERIES MANAGEMENT. FURTHER STEPS INVOLVE EXPLORING THE

CHANGES IN PHENOLOGY ARE AN ECOLOGICAL RESPONSE TO CLIMATE CHANGES, IN ADDITION TO OTHER FACTORS THAT MAY STRESS OR DAMPEN PHENOLOGICAL RESPONSES. FOR THIS STUDY, WE INVESTIGATED HOW CLIMATE VARIABILITY CAN AFFECT THE PHENOLOGY OF THE REPRODUCTIVE PROCESS OF THE ANCHOVY ENGRAULIS RINGENS. WE USED 29 YEARS OF SEA SURFACE TEMPERATURE (SST) DATA AND BIOLOGICAL INFORMATION FROM NORTHERN CHILE STOCK, PARTICULARLY, GONADOSOMATIC INDEX (GI), BODY CONDITION (K), AND MEAN WEIGHT (MTW) BETWEEN 1988 AND 2017. THE BREAKS FOR ADDITIVE SEASON AND TREND (BFAST) METHOD WAS APPLIED TO SST TO ESTIMATE SEASONAL BREAKS AND TO CORRELATE THEM WITH THE SEASONALITY OF THE GI. SEASONALITY AND TREND WERE EXTRACTED FROM THE SERIES TO EVALUATE THEM AS CO-VARIABLES IN GAM AND GLM MODELS IN THE EXPLANATION OF THE GI VARIABILITY. THE GAM MODEL EXPLAINED 56% OF THE VARIANCE, BECAUSE IT RESCUES THE NONLINEAR RELATIONSHIPS OF THE VARIABLES. THE SEASONALITY OF THE TEMPERATURE EXPLAINED 40%, FOLLOWED BY THE BODY CONDITION OF THE FISH (10%). BFAST RESULTS INDICATE A SEASONAL CHANGE IN SST, RECORDING THREE PERIODS: PRIOR TO 1993, 1994?1998 AND AFTER 2009. THIS SEASONAL CHANGE IN THE SST DETERMINES A DELAY IN THE START AND THE MAXIMUM IN THE GI. THE K PRESENTED A NEGATIVE RELATIONSHIP SUCH AS THE MTW, ASSOCIATED WITH ENERGY EXPENDITURE DURING THE REPRODUCTIVE PERIOD. FACED WITH PROJECTIONS OF CLIMATE CHANGE, THE EFFECTS OF THE DECOUPLING BETWEEN LARVAE AND THE ABUNDANCE DURING SPRING ARE NOT KNOWN; THEREFORE, KNOWING THE MECHANISMS THAT CONTROL PHENOLOGY CAN IMPROVE OUR CAPACITY TO MONITOR AND MANAGE MARINE RESOURCES UNDER CLIMATE CHANGE.

IN THIS PAPER, WE STUDY FURTHER PROPERTIES OF THE MODIFIED SKEW-NORMAL-CAUCHY (MSNC) DISTRIBUTION. MSNC DISTRIBUTION CORRESPONDS TO A REFORMULATION OF SKEW-NORMAL-CAUCHY DISTRIBUTION THAT ALLOWS TO OBTAIN A NON-SINGULAR FISHER INFORMATION MATRIX AT SKEWNESS PARAMETER EQUAL ZERO. WE SUGGEST A HIERARCHICAL REPRESENTATION WHICH ALLOWS ALTERNATIVE DERIVATIONS FOR MOMENTS GENERATING FUNCTION, MOMENTS, AND SKEWNESS AND KURTOSIS COEFFICIENTS. AS AN APPLICATION, WE DEVELOP HYPOTHESIS TESTING FOR NORMALITY CONSIDERING THE KULLBACK-LEIBLER DIVERGENCE BETWEEN MSNC DISTRIBUTION AND THE NORMAL ONE. FINALLY, WE APPLY THIS RESULT TO CONDITION FACTOR TIME SERIES OF SHORTFIN MAKO SHARKS OFF NORTHERN CHILE.

IN THIS PAPER, WE EXAMINE THE FINITE MIXTURE (FM) MODEL WITH A FLEXIBLE CLASS OF TWO-PIECE DISTRIBUTIONS BASED ON THE SCALE MIXTURES OF NORMAL (TP-SMN) FAMILY COMPONENTS. THIS FAMILY ALLOWS THE DEVELOPMENT OF A ROBUST ESTIMATION OF FM MODELS. THE TP-SMN IS A RICH CLASS OF DISTRIBUTIONS THAT COVERS SYMMETRIC/ASYMMETRIC AND LIGHT/HEAVY TAILED DISTRIBUTIONS. IT REPRESENTS AN ALTERNATIVE FAMILY TO THE WELL-KNOWN SCALE MIXTURES OF THE SKEW NORMAL (SMSN) FAMILY STUDIED BY BRANCO AND DEY (2001). ALSO, THE TP-SMN COVERS THE SMN (NORMAL, T, SLASH, AND CONTAMINATED NORMAL DISTRIBUTIONS) AS THE SYMMETRIC MEMBERS AND TWO-PIECE VERSIONS OF THEM AS ASYMMETRIC MEMBERS. A KEY FEATURE OF THIS STUDY IS USING A SUITABLE HIERARCHICAL REPRESENTATION OF THE FAMILY TO OBTAIN MAXIMUM LIKELIHOOD ESTIMATES OF MODEL PARAMETERS VIA AN EM-TYPE ALGORITHM. THE PERFORMANCES OF THE PROPOSED ROBUST MODEL ARE DEMONSTRATED USING SIMULATED AND REAL DATA, AND THEN COMPARED TO OTHER FINITE MIXTURE OF SMSN MODELS.

SEA URCHIN (LOXECHINUS ALBUS) IS ONE OF THE MOST ECONOMICALLY IMPORTANT SPECIES IN THE NORTHEAST OF CHILEAN PATAGONIA, FORMING PART OF THE HIGHLY DIVERSE BENTHIC COMMUNITY. THIS RESOURCE IS BEING HARVESTED UNDER SELECTIVE FISHING PRESSURE, WHICH SUPPRESSES GROWTH RATES. IN RESPONSE, THE NATIONAL STANDARDS INSTITUTE ESTABLISHED REGULATION 44 AS A QUALITY CONTROL MEASURE, BASED ON A SAMPLING APPROACH CONSIDERING THE PERCENTAGE OF SEA URCHIN UNDER THE MINIMUM LEGAL SIZE (UMLS) THROUGH AN ACCEPTANCE SAMPLING PLAN. IN 2019, THE CHILEAN UNDERSECRETARY OF FISHERIES AND AQUACULTURE (SUBPESCA), UNDER EXEMPT RESOLUTION NO. 910, RULED THAT ANY VESSEL THAT LANDED 15% WITH SEA URCHIN OF 6.5 CM UMLS OF THE TOTAL CATCH WEIGHT WILL BE SANCTIONED. IN THIS PAPER, A SAMPLING DESIGN IS PRESENTED TO ESTABLISH CRITERIA REGARDING COMPLIANCE WITH THIS PROVISION. THE PLAN PROVIDES A STATISTICAL METHODOLOGY FOR THE EVALUATION OF THE PERCENTAGE OF UMLS SEA URCHIN, WHICH CORROBORATES AND CERTIFIES THE CURRENT LEGISLATION THAT SANCTIONS AND FINES THE CAPTURE OF SEA URCHIN THAT DOES NOT COMPLY WITH UMLS VALUES OUTLINED IN REGULATION 44. ASSUMING A SYSTEMATIC SAMPLING PLAN AND UNDER ASSUMED UMLS VALUES OF 6.0, 6.5, AND 7.0 CM, IT IS DETERMINED THAT 15% OF TOTAL LANDINGS (MARGIN OF TOLERANCE) OF SEA URCHIN UNDER 6.5 CM IS THE OPTIMAL LEVEL. THUS, A CORRECT SPECIFICATION OF THE UMLS ALLOWS PROTECTING THE MOST VULNERABLE FRACTION OF THE POPULATION FROM OVEREXPLOITATION FOR GROWTH.

THE SKEW-REFLECTED-GOMPERTZ (SRG) DISTRIBUTION, INTRODUCED BY HOSSEINZADEH ET AL. (J. COMPUT. APPL. MATH. (2019) 349, 132?141), PRODUCES TWO-PIECE ASYMMETRIC BEHAVIOR OF THE GOMPERTZ (GZ) DISTRIBUTION, WHICH EXTENDS THE POSITIVE TO A WHOLE DOMINION BY AN EXTRA PARAMETER. THE SRG DISTRIBUTION ALSO PERMITS A BETTER FIT THAN ITS WELL-KNOWN CLASSICAL COMPETITORS, NAMELY THE SKEW-NORMAL AND EPSILON-SKEW-NORMAL DISTRIBUTIONS, FOR DATA WITH A HIGH PRESENCE OF SKEWNESS. IN THIS PAPER, WE STUDY INFORMATION QUANTIFIERS SUCH AS SHANNON AND RÉNYI ENTROPIES, AND KULLBACK?LEIBLER DIVERGENCE IN TERMS OF EXACT EXPRESSIONS OF GZ INFORMATION MEASURES. WE FIND THE ASYMPTOTIC TEST USEFUL TO COMPARE TWO SRG-DISTRIBUTED SAMPLES. FINALLY, AS A REAL-WORLD DATA EXAMPLE, WE APPLY THESE RESULTS TO SOUTH PACIFIC SEA SURFACE TEMPERATURE RECORDS.

THE AIM OF THIS WORK WAS TO EXTEND THE RESULTS OF PEREZ ET AL. (PHYSICA A (2006), 365 (2), 282?288) TO THE TWO-DIMENSIONAL (2D) FRACTIONAL BROWNIAN FIELD. IN PARTICULAR, WE DEFINED SHANNON ENTROPY USING THE WAVELET SPECTRUM FROM WHICH THE HURST EXPONENT IS ESTIMATED BY THE REGRESSION OF THE LOGARITHM OF THE SQUARE COEFFICIENTS OVER THE LEVELS OF RESOLUTIONS. USING THE SAME METHODOLOGY. WE ALSO DEFINED TWO OTHER ENTROPIES IN 2D: TSALLIS AND THE RÉNYI ENTROPIES. A SIMULATION STUDY WAS PERFORMED FOR SHOWING THE ABILITY OF THE METHOD TO CHARACTERIZE 2D (IN THIS CASE, ?=2 ) SELF-SIMILAR PROCESSES.