Association between mean residual life (MRL) and failure rate functions for continuous and discrete lifetime distributions

The purpose of this study was to correct some mistakes in the literature and derive a necessary and sufficient condition for the MRL to follow the roller-coaster pattern of the corresponding failure rate function. It was also desired to find the conditions under which the discrete failure rate function has an upside-down bathtub shape if corresponding MRL function has a bathtub shape. The study showed that if discrete MRL has a bathtub shape, then under some conditions the corresponding failure rate function has an upside-down bathtub shape. Also the study corrected some mistakes in proofs of Tang, Lu and Chew (1999) and established a necessary and sufficient condition for the MRL to follow the roller-coaster pattern of the corresponding failure rate function. Similarly, some mistakes in Gupta and Gupta (2000) are corrected, with the ensuing results being expanded and proved thoroughly to establish the relationship between the crossing points of the failure rate and associated MRL functions. The new results derived in this study will be useful to model various lifetime data that occur in environmental studies, medical research, electronics engineering, and in many other areas of science and technology.

Vertical profiles of environmental parameters measured on discrete water samples collected with Niskin bottles at station TARA_209 during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) was a global survey of ocean ecosystems aboard the Sailing Vessel Tara. It carried out extensive measurements of evironmental conditions and collected plankton (viruses, bacteria, protists and metazoans) for later analysis using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set includes properties of seawater, particulate matter and dissolved matter that were measured from discrete water samples collected with Niskin bottles during the 2009-2013 Tara Oceans expedition. Properties include pigment concentrations from HPLC analysis (10 depths per vertical profile, 25 pigments per depth), the carbonate system (Surface and 400m; pH (total scale), CO2, pCO2, fCO2, HCO3, CO3, Total alkalinity, Total carbon, OmegaAragonite, OmegaCalcite, and dosage Flags), nutrients (10 depths per vertical profile; NO2, PO4, N02/NO3, SI, quality Flags), DOC, CDOM, and dissolved oxygen isotopes. The Service National d'Analyse des Paramètres Océaniques du CO2, at the Université Pierre et Marie Curie, determined CT and AT potentiometrically. More than 200 vertical profiles of these properties were made across the world ocean. DOC, CDOM and dissolved oxygen isotopes are available only for the Arctic Ocean and Arctic Seas (2013).

Vertical profiles of environmental parameters measured on discrete water samples collected with Niskin bottles at station TARA_131 during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) was a global survey of ocean ecosystems aboard the Sailing Vessel Tara. It carried out extensive measurements of evironmental conditions and collected plankton (viruses, bacteria, protists and metazoans) for later analysis using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set includes properties of seawater, particulate matter and dissolved matter that were measured from discrete water samples collected with Niskin bottles during the 2009-2013 Tara Oceans expedition. Properties include pigment concentrations from HPLC analysis (10 depths per vertical profile, 25 pigments per depth), the carbonate system (Surface and 400m; pH (total scale), CO2, pCO2, fCO2, HCO3, CO3, Total alkalinity, Total carbon, OmegaAragonite, OmegaCalcite, and dosage Flags), nutrients (10 depths per vertical profile; NO2, PO4, N02/NO3, SI, quality Flags), DOC, CDOM, and dissolved oxygen isotopes. The Service National d'Analyse des Paramètres Océaniques du CO2, at the Université Pierre et Marie Curie, determined CT and AT potentiometrically. More than 200 vertical profiles of these properties were made across the world ocean. DOC, CDOM and dissolved oxygen isotopes are available only for the Arctic Ocean and Arctic Seas (2013).

Vertical profiles of environmental parameters measured on discrete water samples collected with Niskin bottles at station TARA_132 during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) was a global survey of ocean ecosystems aboard the Sailing Vessel Tara. It carried out extensive measurements of evironmental conditions and collected plankton (viruses, bacteria, protists and metazoans) for later analysis using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set includes properties of seawater, particulate matter and dissolved matter that were measured from discrete water samples collected with Niskin bottles during the 2009-2013 Tara Oceans expedition. Properties include pigment concentrations from HPLC analysis (10 depths per vertical profile, 25 pigments per depth), the carbonate system (Surface and 400m; pH (total scale), CO2, pCO2, fCO2, HCO3, CO3, Total alkalinity, Total carbon, OmegaAragonite, OmegaCalcite, and dosage Flags), nutrients (10 depths per vertical profile; NO2, PO4, N02/NO3, SI, quality Flags), DOC, CDOM, and dissolved oxygen isotopes. The Service National d'Analyse des Paramètres Océaniques du CO2, at the Université Pierre et Marie Curie, determined CT and AT potentiometrically. More than 200 vertical profiles of these properties were made across the world ocean. DOC, CDOM and dissolved oxygen isotopes are available only for the Arctic Ocean and Arctic Seas (2013).

Vertical profiles of environmental parameters measured on discrete water samples collected with Niskin bottles at station TARA_139 during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) was a global survey of ocean ecosystems aboard the Sailing Vessel Tara. It carried out extensive measurements of evironmental conditions and collected plankton (viruses, bacteria, protists and metazoans) for later analysis using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set includes properties of seawater, particulate matter and dissolved matter that were measured from discrete water samples collected with Niskin bottles during the 2009-2013 Tara Oceans expedition. Properties include pigment concentrations from HPLC analysis (10 depths per vertical profile, 25 pigments per depth), the carbonate system (Surface and 400m; pH (total scale), CO2, pCO2, fCO2, HCO3, CO3, Total alkalinity, Total carbon, OmegaAragonite, OmegaCalcite, and dosage Flags), nutrients (10 depths per vertical profile; NO2, PO4, N02/NO3, SI, quality Flags), DOC, CDOM, and dissolved oxygen isotopes. The Service National d'Analyse des Paramètres Océaniques du CO2, at the Université Pierre et Marie Curie, determined CT and AT potentiometrically. More than 200 vertical profiles of these properties were made across the world ocean. DOC, CDOM and dissolved oxygen isotopes are available only for the Arctic Ocean and Arctic Seas (2013).

Vertical profiles of environmental parameters measured on discrete water samples collected with Niskin bottles at station TARA_124 during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) was a global survey of ocean ecosystems aboard the Sailing Vessel Tara. It carried out extensive measurements of evironmental conditions and collected plankton (viruses, bacteria, protists and metazoans) for later analysis using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set includes properties of seawater, particulate matter and dissolved matter that were measured from discrete water samples collected with Niskin bottles during the 2009-2013 Tara Oceans expedition. Properties include pigment concentrations from HPLC analysis (10 depths per vertical profile, 25 pigments per depth), the carbonate system (Surface and 400m; pH (total scale), CO2, pCO2, fCO2, HCO3, CO3, Total alkalinity, Total carbon, OmegaAragonite, OmegaCalcite, and dosage Flags), nutrients (10 depths per vertical profile; NO2, PO4, N02/NO3, SI, quality Flags), DOC, CDOM, and dissolved oxygen isotopes. The Service National d'Analyse des Paramètres Océaniques du CO2, at the Université Pierre et Marie Curie, determined CT and AT potentiometrically. More than 200 vertical profiles of these properties were made across the world ocean. DOC, CDOM and dissolved oxygen isotopes are available only for the Arctic Ocean and Arctic Seas (2013).

Vertical profiles of environmental parameters measured on discrete water samples collected with Niskin bottles at station TARA_125 during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) was a global survey of ocean ecosystems aboard the Sailing Vessel Tara. It carried out extensive measurements of evironmental conditions and collected plankton (viruses, bacteria, protists and metazoans) for later analysis using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set includes properties of seawater, particulate matter and dissolved matter that were measured from discrete water samples collected with Niskin bottles during the 2009-2013 Tara Oceans expedition. Properties include pigment concentrations from HPLC analysis (10 depths per vertical profile, 25 pigments per depth), the carbonate system (Surface and 400m; pH (total scale), CO2, pCO2, fCO2, HCO3, CO3, Total alkalinity, Total carbon, OmegaAragonite, OmegaCalcite, and dosage Flags), nutrients (10 depths per vertical profile; NO2, PO4, N02/NO3, SI, quality Flags), DOC, CDOM, and dissolved oxygen isotopes. The Service National d'Analyse des Paramètres Océaniques du CO2, at the Université Pierre et Marie Curie, determined CT and AT potentiometrically. More than 200 vertical profiles of these properties were made across the world ocean. DOC, CDOM and dissolved oxygen isotopes are available only for the Arctic Ocean and Arctic Seas (2013).

Vertical profiles of environmental parameters measured on discrete water samples collected with Niskin bottles at station TARA_126 during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) was a global survey of ocean ecosystems aboard the Sailing Vessel Tara. It carried out extensive measurements of evironmental conditions and collected plankton (viruses, bacteria, protists and metazoans) for later analysis using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set includes properties of seawater, particulate matter and dissolved matter that were measured from discrete water samples collected with Niskin bottles during the 2009-2013 Tara Oceans expedition. Properties include pigment concentrations from HPLC analysis (10 depths per vertical profile, 25 pigments per depth), the carbonate system (Surface and 400m; pH (total scale), CO2, pCO2, fCO2, HCO3, CO3, Total alkalinity, Total carbon, OmegaAragonite, OmegaCalcite, and dosage Flags), nutrients (10 depths per vertical profile; NO2, PO4, N02/NO3, SI, quality Flags), DOC, CDOM, and dissolved oxygen isotopes. The Service National d'Analyse des Paramètres Océaniques du CO2, at the Université Pierre et Marie Curie, determined CT and AT potentiometrically. More than 200 vertical profiles of these properties were made across the world ocean. DOC, CDOM and dissolved oxygen isotopes are available only for the Arctic Ocean and Arctic Seas (2013).

Vertical profiles of environmental parameters measured on discrete water samples collected with Niskin bottles at station TARA_136 during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) was a global survey of ocean ecosystems aboard the Sailing Vessel Tara. It carried out extensive measurements of evironmental conditions and collected plankton (viruses, bacteria, protists and metazoans) for later analysis using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set includes properties of seawater, particulate matter and dissolved matter that were measured from discrete water samples collected with Niskin bottles during the 2009-2013 Tara Oceans expedition. Properties include pigment concentrations from HPLC analysis (10 depths per vertical profile, 25 pigments per depth), the carbonate system (Surface and 400m; pH (total scale), CO2, pCO2, fCO2, HCO3, CO3, Total alkalinity, Total carbon, OmegaAragonite, OmegaCalcite, and dosage Flags), nutrients (10 depths per vertical profile; NO2, PO4, N02/NO3, SI, quality Flags), DOC, CDOM, and dissolved oxygen isotopes. The Service National d'Analyse des Paramètres Océaniques du CO2, at the Université Pierre et Marie Curie, determined CT and AT potentiometrically. More than 200 vertical profiles of these properties were made across the world ocean. DOC, CDOM and dissolved oxygen isotopes are available only for the Arctic Ocean and Arctic Seas (2013).

Vertical profiles of environmental parameters measured on discrete water samples collected with Niskin bottles at station TARA_138 during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) was a global survey of ocean ecosystems aboard the Sailing Vessel Tara. It carried out extensive measurements of evironmental conditions and collected plankton (viruses, bacteria, protists and metazoans) for later analysis using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set includes properties of seawater, particulate matter and dissolved matter that were measured from discrete water samples collected with Niskin bottles during the 2009-2013 Tara Oceans expedition. Properties include pigment concentrations from HPLC analysis (10 depths per vertical profile, 25 pigments per depth), the carbonate system (Surface and 400m; pH (total scale), CO2, pCO2, fCO2, HCO3, CO3, Total alkalinity, Total carbon, OmegaAragonite, OmegaCalcite, and dosage Flags), nutrients (10 depths per vertical profile; NO2, PO4, N02/NO3, SI, quality Flags), DOC, CDOM, and dissolved oxygen isotopes. The Service National d'Analyse des Paramètres Océaniques du CO2, at the Université Pierre et Marie Curie, determined CT and AT potentiometrically. More than 200 vertical profiles of these properties were made across the world ocean. DOC, CDOM and dissolved oxygen isotopes are available only for the Arctic Ocean and Arctic Seas (2013).

Vertical profiles of environmental parameters measured on discrete water samples collected with Niskin bottles at station TARA_140 during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) was a global survey of ocean ecosystems aboard the Sailing Vessel Tara. It carried out extensive measurements of evironmental conditions and collected plankton (viruses, bacteria, protists and metazoans) for later analysis using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set includes properties of seawater, particulate matter and dissolved matter that were measured from discrete water samples collected with Niskin bottles during the 2009-2013 Tara Oceans expedition. Properties include pigment concentrations from HPLC analysis (10 depths per vertical profile, 25 pigments per depth), the carbonate system (Surface and 400m; pH (total scale), CO2, pCO2, fCO2, HCO3, CO3, Total alkalinity, Total carbon, OmegaAragonite, OmegaCalcite, and dosage Flags), nutrients (10 depths per vertical profile; NO2, PO4, N02/NO3, SI, quality Flags), DOC, CDOM, and dissolved oxygen isotopes. The Service National d'Analyse des Paramètres Océaniques du CO2, at the Université Pierre et Marie Curie, determined CT and AT potentiometrically. More than 200 vertical profiles of these properties were made across the world ocean. DOC, CDOM and dissolved oxygen isotopes are available only for the Arctic Ocean and Arctic Seas (2013).

Vertical profiles of environmental parameters measured on discrete water samples collected with Niskin bottles at station TARA_118 during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) was a global survey of ocean ecosystems aboard the Sailing Vessel Tara. It carried out extensive measurements of evironmental conditions and collected plankton (viruses, bacteria, protists and metazoans) for later analysis using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set includes properties of seawater, particulate matter and dissolved matter that were measured from discrete water samples collected with Niskin bottles during the 2009-2013 Tara Oceans expedition. Properties include pigment concentrations from HPLC analysis (10 depths per vertical profile, 25 pigments per depth), the carbonate system (Surface and 400m; pH (total scale), CO2, pCO2, fCO2, HCO3, CO3, Total alkalinity, Total carbon, OmegaAragonite, OmegaCalcite, and dosage Flags), nutrients (10 depths per vertical profile; NO2, PO4, N02/NO3, SI, quality Flags), DOC, CDOM, and dissolved oxygen isotopes. The Service National d'Analyse des Paramètres Océaniques du CO2, at the Université Pierre et Marie Curie, determined CT and AT potentiometrically. More than 200 vertical profiles of these properties were made across the world ocean. DOC, CDOM and dissolved oxygen isotopes are available only for the Arctic Ocean and Arctic Seas (2013).

Vertical profiles of environmental parameters measured on discrete water samples collected with Niskin bottles at station TARA_120 during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) was a global survey of ocean ecosystems aboard the Sailing Vessel Tara. It carried out extensive measurements of evironmental conditions and collected plankton (viruses, bacteria, protists and metazoans) for later analysis using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set includes properties of seawater, particulate matter and dissolved matter that were measured from discrete water samples collected with Niskin bottles during the 2009-2013 Tara Oceans expedition. Properties include pigment concentrations from HPLC analysis (10 depths per vertical profile, 25 pigments per depth), the carbonate system (Surface and 400m; pH (total scale), CO2, pCO2, fCO2, HCO3, CO3, Total alkalinity, Total carbon, OmegaAragonite, OmegaCalcite, and dosage Flags), nutrients (10 depths per vertical profile; NO2, PO4, N02/NO3, SI, quality Flags), DOC, CDOM, and dissolved oxygen isotopes. The Service National d'Analyse des Paramètres Océaniques du CO2, at the Université Pierre et Marie Curie, determined CT and AT potentiometrically. More than 200 vertical profiles of these properties were made across the world ocean. DOC, CDOM and dissolved oxygen isotopes are available only for the Arctic Ocean and Arctic Seas (2013).

Vertical profiles of environmental parameters measured on discrete water samples collected with Niskin bottles at station TARA_121 during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) was a global survey of ocean ecosystems aboard the Sailing Vessel Tara. It carried out extensive measurements of evironmental conditions and collected plankton (viruses, bacteria, protists and metazoans) for later analysis using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set includes properties of seawater, particulate matter and dissolved matter that were measured from discrete water samples collected with Niskin bottles during the 2009-2013 Tara Oceans expedition. Properties include pigment concentrations from HPLC analysis (10 depths per vertical profile, 25 pigments per depth), the carbonate system (Surface and 400m; pH (total scale), CO2, pCO2, fCO2, HCO3, CO3, Total alkalinity, Total carbon, OmegaAragonite, OmegaCalcite, and dosage Flags), nutrients (10 depths per vertical profile; NO2, PO4, N02/NO3, SI, quality Flags), DOC, CDOM, and dissolved oxygen isotopes. The Service National d'Analyse des Paramètres Océaniques du CO2, at the Université Pierre et Marie Curie, determined CT and AT potentiometrically. More than 200 vertical profiles of these properties were made across the world ocean. DOC, CDOM and dissolved oxygen isotopes are available only for the Arctic Ocean and Arctic Seas (2013).

Vertical profiles of environmental parameters measured on discrete water samples collected with Niskin bottles at station TARA_141 during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) was a global survey of ocean ecosystems aboard the Sailing Vessel Tara. It carried out extensive measurements of evironmental conditions and collected plankton (viruses, bacteria, protists and metazoans) for later analysis using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set includes properties of seawater, particulate matter and dissolved matter that were measured from discrete water samples collected with Niskin bottles during the 2009-2013 Tara Oceans expedition. Properties include pigment concentrations from HPLC analysis (10 depths per vertical profile, 25 pigments per depth), the carbonate system (Surface and 400m; pH (total scale), CO2, pCO2, fCO2, HCO3, CO3, Total alkalinity, Total carbon, OmegaAragonite, OmegaCalcite, and dosage Flags), nutrients (10 depths per vertical profile; NO2, PO4, N02/NO3, SI, quality Flags), DOC, CDOM, and dissolved oxygen isotopes. The Service National d'Analyse des Paramètres Océaniques du CO2, at the Université Pierre et Marie Curie, determined CT and AT potentiometrically. More than 200 vertical profiles of these properties were made across the world ocean. DOC, CDOM and dissolved oxygen isotopes are available only for the Arctic Ocean and Arctic Seas (2013).